PENCOYD 
 
 UC-NRLF 
 
 AND 
 
 STEEI 
 
 WILEY & SONS 
 
 1 
 

 
 LIBRARY 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Received .-*^rK><**<*& 188 6. 
 
 Accessions No.^?'*-*- Shelf fib. 
 
 e*- 
 
-umVVff 
 
 WROUGHT IRON AND -STEEL 
 
 IN 
 
 CONSTRUCTION. 
 
 CONVENIENT RULES, FORMULAE, AND TABLES FOR THB 
 STRENGTH OF WROUGHT IRON SHAPES USED AS 
 BEAMS, STRUTS, SHAFTS, ETC., MANUFAC- 
 TURED BY THE PENCOYD IRON WORKS. 
 
 SECOND EDITION, REVISED AND ENLARGED. 
 
 THE. 
 
 uim SRSITT 
 
 >RK. 
 
 JOHN WILEY & SONS, 
 15 ASTOE PLACE, 
 
 1885. 
 
COPYRIGHT, 1884, 
 BT A. & P. ROBERTS & CO. 
 
PREFACE. 
 
 To Engineers and Builders in Iron and Steel this volume is 
 presented, with the hope that it may be of assistance to them in 
 their daily labors, and afford information upon some points 
 which have not heretofore been put in published form. It has 
 been the aim of the author to eliminate as far as possible mat- 
 ters of theory from statements of facts, that, where conflict of 
 opinion may arise, each one may draw his own conclusions. It 
 was considered advisable to treat only of subjects relating to 
 Iron and Steel, referring to any of the numerous engineers' 
 pocket-books for information upon outside matters. 
 
 As far as possible, doubtful points were corroborated by ex- 
 periments, and especially Ihe' article upon "Struts " is based 
 upon the results of several hundred carefully conducted experi- 
 ments at Pencoyd, for more detailed information concerning 
 which we would refer to two papers by Mr. Jas. Christie, pub- 
 lished in the Transactions of the American Society of Civil En- 
 gineers, entitled, " Experiments on the Strength of Wrought 
 Iron Struts," and, " The Strength and Elasticity of Structural 
 Steel," wherein the above experiments are fully described. 
 Hereafter should errors be detected by a more perfect knowledge 
 of the physical properties of the materials treated of, we shall 
 be glad to acknowledge the same, but now offer the following 
 pages as the best results we are able to obtain from present 
 practice. 
 
 A. & P. ROBERTS & CO. 
 
 PENCOTD, May, 1884. 
 
PREFACE TO SECOND EDITION. 
 
 IN preparing the Second Edition for the press we have cor- 
 rected some small errors occurring in various places in the first 
 edition, which were discovered after its publication. A few new 
 tables of weights of separators for beams, of bolts, nuts and 
 rivets, which were deemed useful in architectural calculations, 
 have been added. Some additional shapes are described, and 
 several old sections of beams and channels changed to more effi- 
 cient forms, by better distribution of material in the flanges. 
 At the present writing we have no alterations to make in our 
 conclusions in regard to steel, our experiments up to date seem- 
 ing to confirm our results as then announced. 
 
 A. & . ROBERTS & CO. 
 PENCOYD, January, 1885. 
 
PKEFACE TO THIRD EDITION. 
 
 MOKE than a year has elapsed since the publication of the first 
 edition of this little volume, and we are now preparing a third 
 for the press. A few new sections have been added and several 
 errors overlooked in the earlier editions corrected, so that we 
 believe very few, if any, now exist. Our conclusions in regard 
 to struts, based upon Mr. Christie's experiments, have stood the 
 test of publication and criticism, and we think at this day can 
 be said to have more fully the stamp of authority than when 
 first issued. We trust this Hand Book has and will continue to 
 be of value to all who daily use wrought iron and steel in con- 
 struction. 
 
 A. & P. ROBERTS & CO. 
 
 PEKCOYD, July, 1885. 
 
CONTENTS. 
 
 PAGES 
 
 TABLES OF DIMENSIONS 1-16 
 
 STRENGTH OF WROUGHT IRON 17-23 
 
 STRUCTURAL STEEL 24-31 
 
 STRENGTH OF IRON BEAMS 32-39 
 
 TABLES FOR I BEAMS 40-45 
 
 TABLES FOR CHANNEL BEAMS 46-49 
 
 TABLES FOR DECK BEAMS 50, 51 
 
 IRON FLOOR BEAMS 52-55 
 
 TABLES FOR FLOOR BEAMS 56-62 
 
 BEAMS SUPPORTING BRICK ARCHES AND 
 
 WALLS 63-66 
 
 APPROXIMATE FORMULAE FOR BEAMS 67-77 
 
 BENDING MOMENTS AND DEFLECTIONS 78-81 
 
 BEAMS SUPPORTING IRREGULAR LOADS 82-84 
 
 BEAMS SUBJECT TO BENDING AND COM- 
 
 PRESSION 84-87 
 
 ELEMENTS OF STRUCTURAL SHAPES 87-91 
 
 TABLES OF ELEMENTS 92-101 
 
 MOMENTS OF INERTIA 102-111 
 
 RADII OF GYRATION 112-113 
 
 ROLLED STRUTS 114-153 
 
 TABLES OF I BEAM STRUTS 124-134 
 
 " ANGLE " 138-140 
 
 " TEE " 142,143 
 
 " CHANNEL STRUTS 144-153 
 
 COLUMNS.. ..154-159 
 
VI CONTENTS. 
 
 PAGES 
 
 EIVETS AND PINS 160-162 
 
 STRESSES IN FRAMED STRUCTURES 163-169 
 
 WROUGHT IRON SHAFTING 170-177 
 
 PROPERTIES OF CIRCLES 178-183 
 
 WEIGHT OF ROLLED IRON 184, 185 
 
 DECIMAL EQUIVALENTS FOR FRACTIONS 186 
 
 ILLUSTRATIONS 
 
 For a full detail of the contents see Index. 
 
UNIVERSITY 
 
 WKOUGHT IRON AND STEEL IN 
 CONSTRUCTION. 
 
 TABLES OF DIMENSIONS. 
 
 THE following tables give the principal dimensions of the 
 standard shapes of structural iron and steel rolled at Pencoyd. 
 
 Further particulars of the sections will be found in the illus- 
 trations at the end of the book. 
 
 For beams and channels the least and greatest sections of 
 each size are described in the preliminary tables. Any inter- 
 mediate sectional areas between the maximum and minimum can 
 be rolled, but the flanges remain unaltered, the web only being 
 thickened. The weights per yard corresponding to increased 
 web thicknesses are given in annexed tables. For angles, any 
 thickness between the maximum and minimum can be rolled, 
 corresponding weights for the principal intermediate thicknesses 
 being given in the tables. 
 
 The legs of angles increase slightly in width as the thickness 
 is increased. This renders the actual weights corresponding to 
 given thickness somewhat uncertain. Therefore either the de- 
 sired thickness or weight per yard should be specified, but not 
 both. (The methods of altering the thickness of the foregoing 
 sections, are illustrated in plate No. 28.) The cross-hatched 
 sections represent the least areas, and the blank section the added 
 thickness. 
 
 Tee sections cannot be altered from the standard as given in 
 the tables. Flat bars can be rolled to any thickness between the 
 limits given in the list. 
 
2 WBOUGHT IKON AND STEEL. 
 
 SIZES OF MINIMUM AND MAXIMUM SECTIONS. 
 
 PENCOYD 
 
 BEAMS. 
 
 
 , 
 
 
 1. 
 
 f. 
 
 1/0 
 
 ^ 
 
 1 
 
 1 
 
 a 
 
 B 
 
 q 
 
 1 
 
 o> 
 
 
 fl 
 
 ^ j 
 
 ^| 
 
 Erfs 
 
 
 o 
 
 ii 
 u 
 
 3 
 
 c 
 
 g ^ 
 
 S >> 
 
 5 ^ 
 
 S " 
 
 P ' i 
 
 S^ 
 
 X| 
 
 ^ 
 
 fc 
 
 1 
 
 .5 
 
 Jl, 
 '5 
 
 -4 
 
 !! 
 
 ll 
 
 F 
 
 II 
 
 M 
 
 | 
 
 EH 
 
 0) 
 
 6 
 
 55 
 
 
 * 
 
 i 
 
 *, 
 
 
 
 S 
 
 si 
 S 
 
 ^ 
 
 
 A 
 
 
 
 B 
 
 B 
 
 c 
 
 C 
 
 D 
 
 E 
 
 i 
 
 2 
 
 15 
 15 
 
 200 
 145 
 
 233 
 
 201 
 
 i 
 
 y 
 
 5| 
 
 54 
 
 i 
 
 ijL 
 
 f 
 
 312 
 412 
 
 168 
 120 
 
 194 
 
 1(33 
 
 1! 
 
 A 
 
 5 t, 
 
 511 
 
 i 
 
 li 
 
 M 
 
 5 
 
 101 
 
 134 
 
 161 
 
 M 
 
 it 
 
 5 L 
 
 5 
 
 li- 
 
 fi 
 
 f 
 
 Kt 
 
 108 
 89 
 
 135 
 109 
 
 8 
 
 If 
 
 3 
 
 Mi 
 
 lt 
 
 M 
 
 S 
 
 7 
 
 10 
 
 112 
 
 137 
 
 * 
 
 1 
 
 4-| 
 
 4] 
 
 IT? 
 
 ^ 
 
 8 
 
 10 
 
 90 
 
 106 
 
 M 
 
 
 4$ 
 
 
 f^ 
 
 H 
 
 9 
 
 9 
 
 90 
 
 122 
 
 if 
 
 f 
 
 4 
 
 4i| 
 
 ti 
 
 ^. 
 
 10 
 
 9 
 
 70 
 
 88 
 
 
 1 
 
 
 4H 
 
 
 f 
 
 11 
 
 8 
 
 81 
 
 li,9 
 
 32 
 
 4 
 
 44 
 
 41^. 
 
 i 
 
 S 
 
 12 
 
 8 
 
 65 
 
 75 
 
 Tb<- 
 
 fb- 
 
 4 
 
 it 
 
 t 
 
 f 
 
 13 
 
 7 
 
 65 
 
 88 
 
 Vs 
 
 | 
 
 8|S 
 
 4| 
 
 i 
 
 if 
 
 14 7 
 
 51 
 
 88 
 
 1 
 
 | 
 
 
 4i 
 
 1 
 
 I 
 
 15 
 
 6 
 
 50 
 
 63 
 
 it 
 
 1 
 
 3;T2 
 
 3f 
 
 ii 
 
 ft 
 
 16 
 
 6 
 
 40 
 
 63 
 
 
 f 
 
 3 
 
 
 H 
 
 fi 
 
 17 
 
 5 
 
 34 
 
 40 
 
 "Ftf 
 
 iV 
 
 2|i 
 
 2H 
 
 ^ 
 
 
 18 
 
 5 
 
 30 
 
 40 
 
 3 T 2 
 
 -f ff 
 
 21 
 
 2H 
 
 i 
 
 4 
 
 19 
 
 4 
 
 28 
 
 88 
 
 -L 
 
 i 
 
 O'i 
 
 3 
 
 ^ 
 
 _ti 
 
 20 
 
 4 
 
 18.5 
 
 21.5 
 
 | 
 
 i 
 
 2 
 
 
 t 
 
 /2 
 
 21 
 
 3 
 
 23 
 
 28.6 
 
 .1 
 
 iV 
 
 2^ 
 
 2U 
 
 1^6 
 
 -L 
 
 22 
 
 3 
 
 17 
 
 21.7 
 
 , 8 
 
 A 
 
 24 
 
 
 8 
 
 
 
 The width of the flange varies directly with the thickness 
 of the web. 
 
TABLES OF DIMENSIONS. 
 
 WEIGHTS OF VARIOUS WEB THICKNESSES. 
 
 PENCOYD 
 
 BEAMS. 
 
 Chart Number. 
 
 to to 1 Ci or J Depth in inches. 
 
 - MI* | Minimum Web Thick- 
 ness. 
 
 Minimum Weight per 
 yard. 
 
 APPROXIMATE WEIGHT IN POUNDS PER YARD FOR EACH 
 THICKNESS OP WEB IN INCHES. 
 
 (Calculated upon the basis that one Cubic Foot of Iron 
 weighs 480 Ibs.) 
 
 1 
 
 A 
 
 a. 
 
 A 
 
 * 
 
 5 
 
 8 
 
 t 
 
 i 
 
 1 
 
 2 
 
 8 
 
 4 
 
 200.0 
 145.0 
 
 
 
 
 
 
 
 214.0 
 192.0 
 
 233.0 
 
 
 
 
 145.0 
 
 154.5 
 
 173.0 
 
 
 
 
 fl 
 
 168.0 
 120.0 
 
 
 
 
 
 
 
 179.0 
 155.5 
 
 194.0 
 
 
 
 
 
 125.5 
 
 140.5 
 
 
 
 
 
 
 5 
 54 
 6 
 
 1 
 
 if 
 if 
 
 H 
 
 134.4 
 108.3 
 89.3 
 
 
 
 
 
 137.7 
 118.1 
 105.8 
 
 150.8 
 131.2 
 
 
 
 
 
 
 111.6 
 99.2 
 
 
 
 
 
 92.6 
 
 
 
 
 
 
 
 
 7 
 8 
 
 9 
 10 
 
 11 
 12 
 
 10 
 10 
 
 4 
 
 111.7 
 90.4 
 
 
 
 
 
 111.7 
 106.0 
 
 124.2 
 
 136.7 
 
 
 
 93.6 
 
 99.8 
 
 
 
 
 
 
 
 
 
 9 
 9 
 
 8 
 8 
 
 c-J-cd- 
 
 *-|CK.|W 
 
 90.7 
 69.8 
 
 81.4 
 65.3 
 
 
 
 93.5 
 
 82.4 
 
 99.1 
 
 88.1 
 
 110.4 
 
 121.6 
 
 
 
 71.2 
 
 76.8 
 
 
 
 
 
 S 
 
 83.9 
 75.3 
 
 88.9 
 
 98.9 
 
 108.9 
 
 
 
 65.3 
 
 70.3 
 
 
 
 
 
 
 13 
 
 14 
 
 7 
 
 7 
 
 6 
 
 6 
 
 1! 
 
 65.8 
 51.4 
 
 52^5 
 
 56.9 
 
 61 .'2 
 
 65.8 
 65.6 
 
 70.2 
 70.0 
 
 78.9 
 78.7 
 
 87.7 
 87 5 
 
 
 
 
 
 15 
 
 16 
 
 ii 
 
 50.0 
 40.0 
 
 
 
 
 53.0 
 51.0 
 
 55.5 
 55.0 
 
 63.0 
 63.0 
 
 
 
 40.0 
 
 44.0 
 
 47.5 
 
 
 
 
 
 17 
 
 18 
 
 5 
 5 
 
 t 
 
 34.0 
 30.0 
 
 aiis 
 
 34.0 
 
 34.0 
 
 37.0 
 37.8 
 
 40.0 
 40.9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 19 
 
 20 
 
 4 
 4 
 
 4 
 
 28.0 
 18.5 
 
 28 
 21.5 
 
 30.5 
 
 33.0 
 
 35.5 
 
 38.0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 21 
 22 
 
 3 
 3 
 
 A 
 
 23 
 17.0 
 
 28 
 
 19^8 
 
 24.8 
 21.7 
 
 26.7 
 
 28.6 
 
 
 
 
 
 
 
 
 
 Beams of any weight between the minimum and maximum 
 per yard, given in the table, can be furnished. 
 
 weight 
 
4 WKOUGHT IRON AND STEEL. 
 
 SIZES OF MINIMUM AND MAXIMUM SECTIONS. 
 
 PENOOYD 
 
 Q 
 
 B 
 
 i, CHANNELS. 
 
 
 
 I 
 
 I 
 
 ja 
 
 0) . 
 
 
 
 | 
 
 cs 
 
 3 
 
 i 
 
 I 
 
 1 
 
 j 
 
 fe'S 
 
 ^T3 
 
 
 ^ OD 
 
 
 E - 
 
 1 
 
 1 
 
 Chart Nun 
 
 Size in inc 
 
 Minimum 
 per ya 
 
 Maximum 
 perya 
 
 Minimum 
 Thicknf 
 
 Maximum 
 ThickiK 
 
 Minimum 
 Width 
 
 Maximum 
 Width 
 
 H 
 
 Flange Thi 
 
 
 A 
 
 
 
 B 
 
 B 
 
 C 
 
 C 
 
 D 
 
 E 
 
 30 
 
 15 
 
 139.0 
 
 204.5 
 
 A 
 
 1 
 
 4 
 
 41 
 
 1 
 
 8 
 
 31 
 
 12 
 
 88 5 
 
 160.0 
 
 if 
 
 1 
 
 2f 
 
 3U 
 
 1 
 
 A 
 
 32 12 
 
 60.0 
 
 101.5 
 
 
 jj 
 
 m 
 
 i! 
 
 i 
 
 U 
 
 34 10 
 
 60.0 
 
 106.0 
 
 A 
 
 | 
 
 2Af 
 
 3iV 
 
 T6 
 
 A 
 
 35 10 
 
 49.0 
 
 86.5 
 
 
 5 1 2^ 
 
 2 4 
 
 i 
 
 2 
 
 36 
 
 9 
 
 53.0 
 
 92.0 
 
 j^. 
 
 a i 2-V 
 
 2 7 ? 
 
 a 
 
 _1| 
 
 37 
 
 9 
 
 37.0 
 
 61.0 
 
 it 
 
 i 
 
 2fi- 4 - 
 
 241 
 
 Ii 
 
 64 
 
 38 
 39 
 
 8 
 8 
 
 43.0 
 30.0 
 
 80.5 
 r>4.0 
 
 A 
 If 
 
 . | 
 
 85 
 2 
 
 n 
 
 .4.-1 
 
 11 
 
 H 
 
 40 
 41 
 
 7 
 7 
 
 41. 
 26.0 
 
 73.0 
 49.0 
 
 S 
 
 | 
 
 1 
 
 2A 
 
 1 
 
 i 
 
 42 
 
 6 
 
 31.9 
 
 54.4 
 
 1 
 
 fi 
 
 2| 
 
 2$ 
 
 A 
 
 A 
 
 43 
 
 6 
 
 27.6 
 
 50.1 
 
 -L 
 
 5 
 
 2 
 
 2? 
 
 ii 
 
 1 
 
 44 
 
 6 
 
 22.7 
 
 39.6 
 
 Ji 
 
 | 
 
 If 
 
 2:,V 
 
 
 ft 
 
 45 
 
 5 
 
 27.3 46.0 
 
 ^ 
 
 | 
 
 2 
 
 2S 
 
 it 
 
 
 46 
 
 5 
 
 18.8 32.9 
 
 A 
 
 i 
 
 15. 
 
 Iff 
 
 1 
 
 tV 
 
 47 
 
 4 
 
 21.5 31.5 
 
 i 
 
 -1- 
 
 1H 
 
 lit 
 
 U 
 
 i 
 
 48 
 
 4 
 
 17.5 23.7 
 
 A 
 
 | 
 
 
 
 i* 
 
 T 
 
 49 
 
 3 
 
 15.2 18.9 
 
 A 
 
 H 
 
 1H 
 
 Ifi 
 
 H 
 
 'i 
 
 50 
 
 
 
 11.3 11.3 
 
 j 
 
 4 
 
 i 
 
 H 
 
 If 
 
 i 
 
 i 
 
 51 
 
 2 
 
 8.75 10.0 
 
 A 
 
 3^ 
 
 1A 
 
 1A 
 
 A 
 
 A 
 
 52 
 
 If 
 
 3.5 
 
 3.5 
 
 A 
 
 A 
 
 if 
 
 U 
 
 i 
 
 A 
 
 The width of the flange varies directly with the thickness oJ 
 the web. 
 
TABLES OF DIMENSIONS. 5 
 
 WEIGHTS OF VARIOUS WEB THICKNESSES. 
 FENCOYD \ /CHANNELS. 
 
 I Chart Number. 
 
 c 1 Depth in inches. 
 
 -j 1 Minimum Web 
 Thickness. 
 
 Minimum Weight 
 per yard. 
 
 APPROXIMATE WEIGHT IN POUNDS PER YARD FOR EACH 
 THICKNESS OF WEB IN INCHES. 
 
 Calculated upon the basis that one Cubic Foot of Iron 
 weighs 480 Ibs. 
 
 i 
 
 & 
 
 I 
 
 & 
 
 i 
 
 5. 
 
 I 
 
 1 
 
 1 
 
 1 
 
 139.0 
 
 - 
 
 
 
 148.0 
 
 167.0 
 
 186.0 
 
 204.5 
 
 
 
 
 
 
 31 
 
 32 
 
 34 
 35 
 
 12 
 
 12 
 
 10 
 10 
 
 if 
 & 
 
 ~#~ 
 
 88.5 
 60.0 
 
 
 
 
 92.0 
 79.0 
 
 100.0 
 86.5 
 
 115.0 
 101.5 
 
 130.0 
 
 145.0 
 
 160.0 
 
 49!6 
 
 64.0 
 
 63.0 
 55.0 
 
 71.5 
 
 60.0 
 49.0 
 
 69.0 
 61.5 
 
 75.5 
 
 67.0 
 
 81.0 
 74.0 
 
 94.0 
 86.5 
 
 106.0 
 
 
 
 92^0 
 
 
 
 30 
 
 37 
 
 9 
 9 
 
 8 
 8 
 
 7 
 7 
 
 fk 
 if 
 
 53 . 
 37.0 
 
 .... 
 
 53.0 
 44.0 
 
 45.5 
 39.0 
 
 58.5 1 64.0 
 49.555.0 
 
 70.0 
 61.0 
 
 81.0 
 
 
 
 
 
 
 
 
 
 38 
 31) 
 
 40 
 41 
 
 A 
 Jl 
 
 43.0 
 30.0 
 
 3i!6 
 
 50.5 
 44.0 
 
 55.5 
 49.0 
 
 51.0 
 44 5 
 
 60.5 
 54.0 
 
 55.0 
 49.0 
 
 70.5 
 
 80.5 
 
 
 
 
 
 64.0 
 
 73.0 
 
 
 
 
 
 ig 
 
 s 
 
 41.0 
 26.0 
 
 3i!s 
 
 42.0 
 36.0 
 
 46.5 
 40.0 
 
 39.4 
 35.1 
 32.1 
 
 33.5 
 2G.6 
 
 26.5 
 23.7 
 
 
 
 
 
 42 
 43 
 44 
 
 45 
 46 
 
 47 
 
 48 
 
 49 
 50 
 
 I 
 
 6 
 
 5 
 5 
 
 4 
 4 
 
 3 
 2i 
 
 A 
 I 
 
 1 
 
 A 
 
 ~& 
 i 
 
 31.9 
 27.6 
 22.7 
 
 27.3 
 
 18.8 
 
 21.5 
 17.5 
 
 15.2 
 11.3 
 
 31.9 
 27.6! 
 
 3 
 
 27.3 
 
 20.4 
 
 21.5 
 18.7 
 
 16.1 
 11.3 
 
 35.6 
 31.41 
 28.3, 
 
 30.4 
 23.5 
 
 24.0 
 21.2 
 
 18.0 
 
 43.1 
 
 38.9 
 35.8 
 
 3S.7 
 29.7 
 
 29.0 
 
 46.9 
 42.6 
 39.6 
 
 54.4 
 50.1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 39.8 
 32.9 
 
 46.0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 31.5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 51 
 52 
 
 2 
 If 
 
 A 
 
 8.75 
 
 9.4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ~ 
 
 A 
 
 3.5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Channels of any weight between 
 weight per yard, given in the table, 
 
 the minimum and maximum 
 can be furnished. 
 
6 WROUGHT IRON AND STEEL. 
 
 SIZES OF MINIMUM AND MAXIMUM SECTIONS. 
 
 PENCOYD 
 
 B 
 
 Pi?DECK BEAMS. 
 
 Chart Number. , 
 
 Size in inches. 
 
 'Ec 
 
 ti 
 
 11 
 
 c 
 
 s 
 
 Maximum Weight 
 per yard. 
 
 Minimum Web 
 Thickness. 
 
 Maximum Web 
 Thickness. 
 
 Minimum Flange 
 Width. 
 
 Maximum Flange 
 Width. 
 
 Minimum Bulb 
 Width. 
 
 Maximum Bulb 
 Width. 
 
 Bulb Depth. 
 
 Flange Thickness. 
 
 Flange Thickness.] 
 
 
 A 
 
 
 
 B 
 
 B 
 
 C 
 
 C 
 
 F 
 
 F 
 
 G 
 
 D 
 
 E 
 
 (>(> 
 
 12 
 
 104.0 
 
 138.0 
 
 H 
 
 tt 
 
 51 
 
 6& 
 
 OJ. 
 
 ''B 
 
 2^i 
 
 If 
 
 M 
 
 if 
 
 Gl 
 
 11 
 
 91.0 
 
 118.0 
 
 1 
 
 | 
 
 5i 
 
 51 
 
 2 
 
 2i 
 
 H 
 
 a 
 
 4 
 
 ft 
 
 62 
 
 10 
 
 80.0 
 
 105.0 
 
 3 
 
 1 
 
 &i 
 
 &i 
 
 ii 
 
 2i 
 
 HI 
 
 H 
 
 ii 
 
 6;] 
 
 9 
 
 72.0 
 
 94.0 
 
 3. 
 
 
 
 B 
 
 H 
 
 5 
 
 5i 
 
 m 
 
 2A- 
 
 Hi 
 
 1 
 
 f 
 
 04 
 
 8 
 
 61.0 
 
 84.0 
 
 ft 
 
 1 
 
 4 
 
 4ff 
 
 m 
 
 m 
 
 1A 
 
 tt 
 
 H 
 
 65 
 
 7 
 
 52.0 
 
 72.0 
 
 H 
 
 | 
 
 41 
 
 4M 
 
 ii 
 
 iii 
 
 1A 
 
 1% 
 
 tV 
 
 GO 
 
 6 
 
 42.0 
 
 57.0 
 
 A 
 
 A 
 
 81 
 
 4 
 
 1A 
 
 1U 
 
 1^ 
 
 H 
 
 A 
 
 67 
 
 5 
 
 34.0 
 
 46.0 
 
 rv 
 
 A 
 
 H 
 
 8| 
 
 iA 
 
 l-i 2 ,; 
 
 -it 
 
 i 
 
 I 
 
TABLES OF DIMENSIONS. 7 
 
 WEIGHTS OF VARIOUS WEB THICKNESSES. 
 
 PENCOYD 
 
 o 
 
 DECK BEAMS. 
 
 Depth in inches. | 
 
 Minimum Web Thick- 
 ness. 
 
 Minimum Weight per 
 yard. 
 
 APPROXIMATE WEIGHT IN POUNDS PER YARD FOR 
 EACH THICKNESS OP WEB IN INCHES. 
 
 Calculated upon the basis that one Cubic Foot of Iron 
 weighs 480 Ibs. 
 
 i 
 
 A 
 
 a 
 
 8 
 
 A 
 
 i 
 
 A 
 
 1 
 
 ti 
 
 12 
 
 i i 
 .j -i 
 
 a 
 
 
 
 104.0 
 
 
 
 
 108.0 
 
 115.0 
 
 123.0 
 
 130.0 
 
 138.0 
 
 
 
 
 11 
 
 91.0 
 
 
 
 91.0 
 
 98.0 
 
 105.0 
 
 111.0 
 
 118.0 
 
 
 
 
 
 
 10 
 
 a. 
 
 80.0 
 
 
 
 80.0 
 
 86.0 
 
 92.0 
 
 99 
 
 105.0 
 
 
 
 
 9 
 
 n 
 
 8 
 
 72.0 
 
 .... 
 
 .... 
 
 72.0 
 
 77.0 
 
 83.0 
 
 89.0 
 
 94.0 
 
 
 
 8 
 7 
 
 & 
 
 61.0 
 
 
 
 64 
 
 69.0 
 
 74.0 
 
 79.0 
 
 84.0 
 
 
 
 
 
 H 
 
 52.0 
 
 
 
 54.0 
 
 58.0 
 
 63.0 
 
 67.0 
 
 72.0 
 
 
 
 42.0 
 
 
 6 
 5 
 
 A 
 
 A 
 
 42.0 
 
 .... 
 
 46.0 
 
 49.0 
 
 53.0 
 
 57.0 
 
 
 
 
 
 84.0 
 
 .... 
 
 34.0 
 
 37.0 
 
 40.0 
 
 43.0 
 
 46.0 
 
 
 
 
 
WROUGHT IRON AND STEEL. 
 
 PENCOYD 
 
 ANGLES. 
 
 EVEN LEGS. 
 
 WEIGHTS PER YARD OF VARIOUS THICKNESSES. 
 One cubic foot weighing 480 Ibs. 
 
 Chart 
 Number. 
 
 SIZE IN 
 INCHES. 
 
 1" 
 
 -.V 
 
 i" 
 
 iV' 
 
 1" 
 
 71.1 
 
 U" 
 
 t" 
 
 ir 
 
 I" 
 
 1" 
 
 120 
 
 6 x6 
 
 
 50.6 
 
 57.5 
 
 64.3 
 
 77.8 
 
 84.4 
 69.4 
 
 90.6 
 
 97.3 
 
 110.0 
 
 121 
 
 5 x5 
 
 
 41.8 
 
 47.5 
 37.5 
 
 53.1 
 
 41.8 
 
 58.6 
 46.1 
 
 (54.0 
 50.3 
 
 74.7 
 
 79.8 
 
 90.0 
 
 122 
 
 4 x4 28.6 
 
 33.1 
 
 54.4 
 
 
 
 
 
 
 
 123 
 
 3x3 
 
 24.8 
 i" 
 
 8 
 
 28.7 
 
 -a," 
 
 32.5 
 
 J." 
 4 
 
 36.2 
 
 A-" 
 
 3D. 8 
 1" 
 
 
 
 
 
 
 iV' 
 
 T 
 
 iV' 
 
 5." 
 
 
 
 124 
 
 3 x3 
 
 
 
 14.4 
 
 17.8 
 
 21.1 
 
 24.3 
 22.1 
 
 27.5 
 
 30.6 
 
 33.6 
 
 
 
 
 
 125 
 
 2Jx23 
 
 
 
 13.1 
 
 16.2 
 
 19.2 
 
 25.0 
 
 
 
 
 
 
 
 
 
 126 
 
 2j x 2i 
 
 
 
 11.9 
 
 14.6 
 13.1 
 
 17.3 
 15.5 
 
 19.9 
 17.8 
 
 22.5 
 
 
 
 
 
 
 
 
 
 
 
 127 
 
 01 v Ol 
 w 4 X ~ 4 
 
 
 
 10.6 
 
 
 
 
 
 
 
 
 128 
 
 2 x2 
 
 
 
 7.1 
 
 9.4 
 
 11.513.6.... 
 
 
 
 
 
 ... . 
 
 
 129 
 
 11*11 
 
 6.2 
 
 8.1 
 
 9.9 
 
 11.7 
 
 
 
 
 
 
 
 
 130 
 
 HxU 
 
 
 
 5.3 
 4.3 
 
 6.9 
 
 5.6 
 
 8.4 
 
 9.8 
 
 
 
 
 
 
 
 
 
 
 131 
 
 lixii 
 
 3.0 
 
 
 
 
 
 
 
 
 
 
 
 
 132 
 
 1 xl 
 
 2.3 
 
 3.4 
 
 4.4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TABLE OF DIMENSIONS. 
 
 PENCOYD 
 
 ANGLES. 
 
 UNEVEN LEGS. 
 
 WEIGHTS PER YARD OF VARIOUS THICKNESSES. 
 One cubic foot weighing 480 Ibs. 
 
 Chart 
 Number. 
 
 SIZE 
 
 IN 
 
 INCHES 
 
 i 
 
 A 
 
 3. 
 
 a 
 
 * 
 
 41. 
 37.4 
 35.1 
 33.0 
 
 \ 
 
 47.5 
 42.5 
 40.0 
 
 ^ 
 
 53.0 
 47.4 
 44.6 
 
 f 
 
 1 
 
 I 
 
 79.8 
 71.1 
 
 1 
 
 90.0 
 80.0 
 
 140 
 
 6 x4 
 
 .... 
 
 58.6 
 52.3 
 49.2 
 46.0 
 
 69.4 
 61.8 
 
 141 
 
 5 x4 
 
 .... 
 
 
 
 32.3 
 30.5 
 
 142 
 
 5 xS^ 
 
 
 58.1 
 
 143 
 
 5 x3 
 
 .... 
 
 
 28.6 
 
 37.5 
 
 41.7 
 
 54.4 
 
 
 .... 
 
 144 
 
 4x3 
 
 .... 
 
 .... 
 
 26.730.935.0 
 
 S9.0 
 
 43.0 
 
 .... 
 
 
 
 
 145 
 
 4 x3 
 
 
 
 26.7 
 
 CO 935.0 
 
 S9.0J43.0 
 
 
 
 
 
 
 
 
 
 146 
 
 4 x3 
 
 .... 
 
 21.024.8^8.732.536.239.8 
 
 
 
 _ 
 
 147 
 
 3^x3 
 
 
 .... 
 
 23.026.5 
 
 30.033.4 
 
 36.7 
 
 148 
 
 3 x2i 
 
 11.9 
 
 16.219.222.125.0 
 14.617.319.9 I 22.5 
 
 
 
 149 3 x2 
 
 
 
 
 
 
 
 150 3x2 
 
 
 17.8 
 
 21.1 
 34.5 
 
 24 3 
 
 27.5 
 
 
 
 
 
 
 
 
 
 
 85.0 
 
 151 
 
 6 x3 
 
 ... 
 
 39.645.0 ! 
 
 50.3 
 
 55.5165.6 
 
 | 
 
 5.5 
 
 152 
 153 
 
 6|x4 
 
 
 
 ~ 
 
 32.3 
 
 44.0 
 37.4 
 
 50.055.9 
 
 61.7 
 
 73.1 
 
 84.295.0 
 
 Si x 3.} 
 
 42.5 
 
 47.4 
 
 52.3 
 61.7 
 
 73.1 
 
 84.2 
 
 95.0 
 
 154 
 
 7 x3 
 
 
 
 
 
 
 
 
 
 
 155 
 
 2^x2 
 
 10.6 
 
 13.1 
 
 15.4 
 
 17.7 
 
 20.0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 156 
 
 aixu 
 
 8.7 
 
 10.7 
 
 12.6 
 
 
 
 
 
 
 
 
 
 
 
 
 157 
 
 2 xl-i 
 
 7.5 
 
 9.2 
 
 10.8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10 
 
 WROUGHT IRON AND STEEL. 
 
 PENCOYD 
 
 ANGLES. 
 
 SQUARE BOOT. 
 
 WEIGHTS PER YARD OF VARIOUS THICKNESSES. 
 One cubic foot weighing 480 Ibs. 
 
 CHART 
 NUMBER. 
 
 160 
 
 SIZE IN 
 
 INCHES. 
 
 i 
 
 A 
 
 i 
 
 ft 
 
 
 
 ft 
 
 i 
 
 A 
 
 I 
 
 4x4 
 
 
 
 
 
 28.6 
 
 33.0 
 
 37.6 
 
 41.8 
 
 46.0 
 
 
 
 
 
 161 
 
 3^x3^ 
 
 
 
 
 20.8 
 
 24.8 
 
 28.7 
 
 32.5 
 
 
 
 
 
 14'. 4 
 
 
 
 162 
 
 3x3 
 
 
 
 17.8 
 
 21.2 
 
 >4.4 
 
 27.5 
 
 
 
 
 
 
 
 163 
 164 
 
 2fx2f 
 
 2^x2i 
 
 
 
 
 
 13.1 
 11.9 
 
 16.2 
 14.6 
 
 19.2 
 
 i7! 
 
 22.1 
 19.9 
 
 25.0 
 
 .... 
 
 
 
 .... 
 
 165 
 166 
 
 3i x 2* 
 
 
 
 10.6 
 
 13.1 
 11.5 
 
 15.5 
 
 17.8 
 
 
 
 
 
 
 
 
 
 
 2x2 
 
 ..... 
 
 ... 
 
 9.4 
 
 13.6 
 
 .... 
 
 .... 
 
 167 
 
 If- a If 
 
 
 
 8.1 
 6.9 
 
 9.9 
 
 8.4 
 
 11.7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 168 
 
 li x H 
 
 .... 
 
 5.3 
 
 169 
 
 U x H 
 
 .... 
 
 4.3 
 
 5.6 
 
 7.0 
 
 .... 
 
 .... 
 
 .... 
 
 ....u... 
 
 170 
 
 1x1 
 
 2.3 
 
 3.4 
 
 4.4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 171 
 
 U x {f 
 
 
 
 5 9 
 
 
 
 
 
 
 
 
 
 
 
TABLES OF DIMENSIONS. 
 
 ; ^ 
 
 11 
 
 PENCOYD 
 
 TEES. 
 
 EVEN LEGS. 
 
 Chart Number. 
 
 Width of base. 
 
 g 
 
 5 
 
 <s 
 
 1 
 
 w 
 
 Thickness of 
 base. 
 
 Thickness of 
 base. 
 
 Thickness of 
 stem. 
 
 Thickness of 
 stem. 
 
 WEIGHT 
 PER YARD. 
 
 
 A 
 
 B 
 
 D 
 
 E 
 
 C 
 
 F 
 
 
 70 
 
 4 
 
 4 
 
 & 
 
 ft 
 
 ^ 
 
 i 
 
 36.51bs. 
 
 71 
 
 9* 
 
 8i 
 
 ft 
 
 i 
 
 iV 
 
 i 
 
 31.01bs. 
 
 72 
 
 3 
 
 3 
 
 H 
 
 if 
 
 -i\ 
 
 i 
 
 SC.Olbs. 
 
 73 
 
 2i 
 
 2i 
 
 if 
 
 if 
 
 H 
 
 if 
 
 19.51bs. 
 
 74 
 
 2* 
 
 2i 
 
 H 
 
 if 
 
 tt 
 
 if 
 
 17.52 Ibs. 
 
 75 
 
 3* 
 
 2i 
 
 i 
 
 3 
 
 
 
 i 
 
 i 
 
 11.751bs. 
 
 76 
 
 2i 
 
 ^ 
 
 i 
 
 1% 
 
 i 
 
 4 
 
 A 
 
 12.0 Ibs. 
 
 77 
 
 2 
 
 2 
 
 i 
 
 4 
 
 ft 
 
 1 
 4 
 
 ft 
 
 10. 5 Ibs. 
 
 78 
 
 if 
 
 If 
 
 ft 
 
 i 
 
 A 
 
 i 
 
 7. libs. 
 
 79 
 
 H 
 
 H 
 
 A 
 
 i 
 
 A 
 
 i 
 
 6.0 Ibs. 
 
 80 
 
 n 
 
 n 
 
 ft 
 
 i 
 
 4 
 
 tV 
 
 i 
 
 4. 5 Ibs. 
 
 81 
 
 i 
 
 i 
 
 A 
 
 i 
 
 A 
 
 i 
 
 3.0 Ibs. 
 
 82 
 
 3 
 
 3 
 
 TO 
 
 1 
 
 ft 
 
 3. 
 
 f 
 
 19. a Ibs. 
 
 83 
 
 3 
 
 3 
 
 2 
 
 ft 
 
 3. 
 
 
 
 ft 
 
 22. 6 Ibs. 
 
 Weights of these sections cannot be varied. 
 
12 
 
 WBOUGHT IKON AND STEEL. 
 
 PENCOYD 
 
 TESS. 
 
 UNEVEN LEGS. 
 
 Chart Number. 
 
 Width of base. 
 
 Height of stem. 
 
 Thickness of 
 base. 
 
 Thickness of 
 base. 
 
 Thickness of 
 stem. 
 
 H 
 
 c g 
 
 I s 
 
 2 
 H 
 
 WEIGHT 
 PER YARD. 
 
 
 A 
 
 B 
 
 D 
 
 E 
 
 C 
 
 F 
 
 
 90 
 
 4i 
 
 8* 
 
 A 
 
 i 
 
 H 
 
 i 
 
 44.51bs. 
 
 91 
 
 4 
 
 8J 
 
 A 
 
 t 
 
 A 
 
 u. . 
 
 4 
 
 41.81bs. 
 
 92 
 
 5 
 
 2i 
 
 1 
 
 | 
 
 A 
 
 g 
 
 30.71bs. 
 
 93 
 
 5 
 
 ft 
 
 A 
 
 A 
 
 A 
 
 1* 
 
 33.01bs. 
 
 94 
 
 4 
 
 3 
 
 a 
 
 
 
 A . 
 
 t 
 
 
 
 25.91bs. 
 
 95 
 
 4 
 
 3 
 
 5 
 
 A 
 
 A 
 
 | 
 
 25.251bs. 
 
 96 
 
 4 
 
 2 
 
 4 
 
 T^ 
 
 t 
 
 1^ 
 
 20.41bs. 
 
 97 
 
 3 
 
 8ft 
 
 A 
 
 i 
 
 iV 
 
 f 
 
 28.25 Ibs. 
 
 98 
 
 3 
 
 8i 
 
 a. 
 
 A 
 
 i 
 
 I 
 
 23.81bs. 
 
 99 
 
 3 
 
 H 
 
 1 
 
 i 
 
 
 4 
 
 i 
 
 11. 2 Ibs. 
 
 ICO 
 
 *$ 
 
 u 
 
 1 
 
 i 
 
 4 
 
 i 
 
 A 
 
 9.1 Ibs. 
 
 101 
 
 2 
 
 H 
 
 . - 4 
 
 3% 
 
 i 
 
 A 
 
 8 . 75 Ibs. 
 
 102 
 
 2 
 
 1 
 
 i 
 
 1 
 4 
 
 i 
 
 :r* 
 
 7.0 Ibs. 
 
 103 
 
 2 
 
 A 
 
 i 
 
 4 
 
 1 
 4 
 
 A 
 
 5 
 
 TiT 
 
 5.88 Ibs. 
 
 104 
 
 2f 
 
 if 
 
 4 
 
 H 
 
 i 
 
 3. 
 4 
 
 18. 75 Ibs. 
 
 105 
 
 2f 
 
 2 
 
 A 
 
 ii 
 
 n 
 
 4 
 
 t 
 
 21.0 Ibs. 
 
 106 
 
 5 
 
 3* 
 
 i 
 
 i 
 
 i* 
 
 | 
 
 48. 4 Ibs. 
 
 107 
 
 5 
 
 4 
 
 i 
 
 i 
 
 i 
 
 a 
 
 44.1 Ibs. 
 
 108 
 
 2* 
 
 i a ff 
 
 | 
 
 i 
 
 A 
 
 ^ 
 
 6. 5 Ibs. 
 
 109 
 
 4 
 
 g 
 
 A 
 
 , 5 . 
 
 A 
 
 i 
 
 38. 5 Ibs. 
 
 110 
 
 3 
 
 2* 
 
 A 
 
 4 
 
 -5- r 
 
 a 
 
 17. 6 Ibs. 
 
 111 
 
 3 
 
 SJft 
 
 a. 
 
 i 
 
 A 
 
 A 
 
 t 
 
 20. 6 Ibs. 
 
 Weights of these sections cannot be varied. 
 
TABLES OF DIMENSIONS. 
 
 13 
 
 PENCOYD 
 
 ANGLE COVERS. 
 
 WEIGHTS PER YARD OF VARIOUS THICKNESSES. 
 
 One cubic fo'ot weighing 480 Ibs. 
 
 CHAKT 
 NUMBER. 
 
 180 
 181 
 
 SIZE IN 
 INCHES. 
 
 3x3 
 
 2f x 2J 
 
 i 
 
 1*6 
 
 i 
 
 14.3 
 13.0 
 11.8 
 10.5 
 
 A 
 
 17.7 
 16.1 
 14.5 
 13.0 
 
 t 
 21.0 
 19.1 
 17.2 
 15.4 
 
 f* 
 
 24.2 
 
 * 
 
 27.4 
 24.9 
 
 < 
 
 ITS 
 
 30.5 
 
 I 
 33.5 
 
 
 
 22.0 
 
 
 
 182 
 183 
 
 2|x2 
 2i- x 2| 
 
 
 
 19.9 
 
 17.7 
 
 22.4 
 
 
 
 
 
 
 
 
 .... 
 
 184 
 
 2x2 
 
 .... 
 
 7.0 
 
 9.3 
 
 11.4 
 
 13.5 
 
 .... 
 
 .... 
 
 .... 
 
 .... 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
WROUGHT IRON AND STEEL. 
 SIZES OF PENCOYD BAR IRON. 
 
 FLATS. 
 
 1 
 
 x 
 
 if inches to f inches. 
 
 2A- 
 
 x 
 
 \\ inches to 2 
 
 inches. 
 
 1 
 
 X 
 
 i 
 
 ( 1 
 
 2| b 
 
 x 
 
 * " It 
 
 ** 
 
 I 7 /? 
 
 X 
 
 ^ 
 
 1 
 
 2 i 
 
 x 
 
 i 2 
 
 tt 
 
 ITU" 
 
 x 
 
 I 
 
 . -^ 
 
 
 X 
 
 i " 2t 
 
 << 
 
 It 
 
 X 
 
 I 
 
 1 
 
 afe 
 
 x 
 
 It " 2t 
 
 
 
 IT\T 
 
 X 
 
 b. 
 
 8 
 
 1 
 
 3 
 
 x 
 
 
 ' at 
 
 
 
 if 
 
 x 
 
 x 
 
 | i 
 
 1 " 
 1 
 
 31 
 
 x 
 
 X 
 
 1| 
 
 3 
 2 
 
 ft 
 
 if 
 
 x 
 
 X 
 
 | 
 
 1 
 
 I 
 
 3t 
 4 
 
 X 
 
 X 
 
 1 
 
 2 
 3t 
 
 <( 
 
 14> 
 
 X 
 
 '1 -jJg- 
 
 ( 
 
 44- 
 
 x 
 
 4" 
 
 2 
 
 ft 
 
 IrV 
 
 x 
 
 tt " iVfr 
 
 * 
 
 5 
 
 x 
 
 ? 
 
 3t 
 
 
 
 It 
 
 x 
 
 "1 " 11 
 
 ( 
 
 6 
 
 X 
 
 i 
 
 ' 3 
 
 t 
 
 l^f 
 
 X 
 
 " I'll? 
 
 ' 
 
 7 
 
 X 
 
 
 3 
 
 < 
 
 !" 
 
 X 
 
 i " IfV 
 
 < 
 
 8 
 
 X 
 
 1 
 
 < 2^ 
 
 f 
 
 If 
 
 X 
 
 JL |i 
 
 < 
 
 9 
 
 X 
 
 i. 
 
 < 2 1 
 
 
 
 lit 
 
 X 
 
 1 " l| 
 
 < 
 
 10 
 
 X 
 
 JL 
 
 ' 21 
 
 t 
 
 2 
 
 If 
 
 X 
 X 
 X 
 
 i " ll , 
 i it 
 
 
 11 
 
 12 
 
 X 
 
 X 
 
 1 
 
 ' l\ 
 
 ~ 
 
 SQUARES. 
 
 t", -iV, f", H", t", it", i", if", i", w, n", w, 
 
 H", 1|", 1|", ir', If", U", 2", 24", 2t", 2|", 3", 3-1", 
 3V, 3|", 4" and 44". 
 
 ROUNDS. 
 
 M", 14", i". If", iV, ti", I!", IS", f", H", tt", 
 H", H", f", Jl", IS". M", i", M", F', H", tt", II". 
 Si", II", i", W, W, life", lt",'iA", W, 1^", 
 
 14", itr, i^", U", i-.v, it", w, if, if", ij", 
 
 2", 2F, 21", 2|", 2t", at", 21", 21-", 3", 8t", 31", 8f", 3f' f 3f", 
 8f", 3|", 4", 44", 41", 4f ", 44", 4f', 4|", 4J", 5", 51", 64", 5|", 
 6", 6^" and 7". 
 
 HALF ROUNDS. 
 
 i", 1", 11", It", 1|" , 2", 21", 2^, 2f", 3", 34" and 34". 
 
MISCELLANEOUS SHAPES. 
 
 15 
 
 Two grades of iron are manufactured, known respectively as 
 " Pencoyd Refined " and " Pencoyd High Test," the former for 
 all ordinary requirements, the latter for tension members of 
 structures and all purposes where a uniform iron of high duc- 
 tility is required. 
 
 10 X AREA IN INCHES = WEIGHT PER YARD IN LBS. 
 
 In any rolled section of wrought iron, the weight in Ibs. per 
 yard, is precisely equal to ten times its sectional area in square 
 inches. 
 
 Consequently, either value being known, the other can be in- 
 stantly obtained. 
 
 AXLES. 
 
 M^ 
 
 U$ 
 
 TT* 
 
 U- 
 
 ' // 
 -W*- 
 
 J 
 
 MASTER CAR BUILDERS' STANDARD-AXLE 
 
 Hammered or rolled axles of iron or steel, centred and 
 straightened with journals forged or rough-turned, made to con- 
 form to specifications and tests. 
 
 STRUCTURAL WORK. 
 
 The fitting, punching, and riveting of structural work exe- 
 cuted, and iron castings furnished to order. 
 
15 WROUGHT IRON AND STEEL. 
 
 MISCELLANEOUS SHAPES. 
 
 CAR BUILDERS' CHANNEL. 
 
 Chart No. 33. 
 Weight per yard = 50 to 55 Ibs. 
 
 TEN-INCH BULB PLATE. 
 
 Chart No. 68. 
 Weight per yard = 62 Ibs. 
 
 MINERS' TRACK RAIL. 
 
 Chart No. 190. 
 Weight per yard = 25 Ibs. 
 
 SPLICE BAR FOR MINERS' TRACK RAIL. 
 
 Chart No. 191. 
 Weight per yard = 5.2 Ibs. 
 
 SLOT RAIL FOR CABLE ROAD. 
 
 Chart No. 192. 
 Weight per yard = 26 Ibs. 
 
 HALF OVALS. 
 
 Chart No. 193 = 4.3 Ibs. per yd. 
 Chart No. 194 = 4.8 Ibs. per yd. 
 
 Channel Rail. Chart No. 195 = 3.5 Ibs. per yard. 
 
 GROOVED BARS. 
 
 Chart No. 196 = 8.4 to 14.7 Ibs. per yard. 
 
 197 = 1 3 5 to 21 . Ibs. per yard. 
 
 " 198 = 20 . 9 to 34 5 Ibs. per yard. 
 
STRENGTH OF WROUGHT IRON. 
 STRENGTH OF WROUGHT IRON. 
 
 17 
 
 The tensile strength of rolled iron varies according to the quality 
 of the material, the mode of manufacture, and the sectional area 
 of the bar. In general terms the ordinary sizes of bars of good 
 material may be accepted as having an ultimate tensile strength 
 of 50,000 Ibs. per square inch of section, an elastic limit of 
 30,000 Ibs., and will stretch 20 per cent, in a length of 8 inches 
 when tested up to rupture. 
 
 It is, however, as easy to produce the smaller sizes yielding 
 results 10 per cent, higher than the above, as it is difficult to 
 make the largest sections with a limit 10 per cent, below the 
 same figures. 
 
 Dividing rolled iron into three classes according to its sectional 
 area, we have: 
 
 I. Bars not exceeding 1$ square inches area. 
 II. Bars from H to 4 square inches area. 
 
 III. Bars from 4 to 8 square inches area. 
 
 For which experiments give the following figures as average 
 results. 
 
 
 TENSILE STRENGTH 
 
 ELASTIC LIMIT 
 
 ELONGATION IN 
 
 CLASS. 
 
 
 
 
 
 PER SQ. INCH. 
 
 PEU SQ. INCH. 
 
 8 INCHES. 
 
 I. 
 
 53,000 Ibs. 
 
 33,000 Ibs. 
 
 25 per cent. 
 
 II. 
 
 50,000 " 
 
 30,000 " 
 
 20 " 
 
 III. 
 
 48,000 " 
 
 28,000 " 
 
 18 " " 
 
 These, however, are only general conclusions, as much depends 
 on the shape of the section, the method of rolling, and the 
 reduction of area from the pile to the finished bar. 
 
 The following tensile tests are actual averages taken from our 
 records, and were made on specimens cut from bars of the sizes 
 and shapes given, and intended for use in bridges, and to con- 
 form to the specifications of the leading railroad companies. 
 2 
 
18 
 
 WROUGHT IRON AND STEEL. 
 
 SIZE AND SHAPE OF 
 BAR. 
 
 Ultimate strength 
 in Ibs. Per Square 
 Inch. 
 
 S| 
 
 ik 
 iifl 
 
 S OB 
 
 s^ 
 
 Per Cent, of 
 Elongation in 8 
 inches. 
 
 Per Cent, of 
 Reduction of 
 Fractured Area. 
 
 
 One-inch rounds. 
 Two-inch rounds. 
 Four-inch rounds. 
 Four-inch flats. 
 Eight-inch flats. 
 Twelve-inch flats. 
 Three-inch angles. 
 Six-inch angles. 
 Flanges of beams 
 Webs of beams. 
 
 52,210 
 50,935 
 
 48,220 
 51,000 
 49,500 
 49,(J80 
 49,000 
 49,160 
 51,840 
 50,130, 
 
 32,150 
 31,800 
 26,640 
 30,000 
 31,500 
 31,560 
 30,500 
 30,150 
 31,560 
 30,150 
 
 26 
 19.8 
 18 
 20.7 
 16 
 15.5 
 17 
 18.1 
 20.1 
 17.7 
 
 39 
 
 
 
 
 
 31 
 '30* 
 
 f to H in- thick. 
 % inches thick. 
 | inches thick. 
 
 
 
 
 
 
 
 
 COMPRESSION. 
 
 The power of wrought iron to resist compression is usually 
 taken as equal to its tensile strength. In the form of flanges for 
 solid beams, this property is exerted to its full capacity, as the 
 adjacent portion of the material in tension sustains the portions 
 in compression from buckling, even when the length of the 
 beam becomes very considerable. But in the form of struts and 
 columns, when the piece becomes of considerable length in pro- 
 portion to its cross-section, failure occurs by bending, or com- 
 bined bending and crushing. (See article on Struts.) Judging 
 from many experiments we have made on bars secured from 
 bending under compressive stress, the elastic limit in compres- 
 sion is a little lower than in tension, but the former not so clearly 
 defined as the latter ; practically they may be considered as 
 equal. 
 
 These results were derived from small sections; in large sections 
 there may be more equality, as some experiments hereafter de- 
 scribed would denote. 
 
 With pressures varying from 25,000 to 35,000 Ibs. per square 
 inch, the elastic limit is attained. With 50,000 Ibs. per square 
 inch a permanent reduction of 2^ per cent, of the length is pro- 
 duced; with 75,000 Ibs. a reduction of 6 per cent, and with 
 
ELASTICITY OF ROLLED IRON. 19 
 
 100,000 Ibs. per square inch the permanent reduction of length 
 is about 8 per cent. These results have a wide range of varia- 
 tion, bufe the figures are the averages of several experiments. 
 
 ELASTICITY OF ROLLED IRON. 
 
 The elasticity of wrought iron, or its ratio of change of length 
 under stress below the elastic limit, varies more extensively than 
 any other property of rolled iron. Experiment shows a varia- 
 tion of over 100 per cent, in extreme cases. 
 
 The modulus of elasticity is an imaginary load, which, suppos- 
 ing the material to be perfectly elastic, would cause the iron to 
 double its length under tension, or to shorten its length one-half 
 under compression, and return to its original length when re- 
 leased from stress. This modulus is usually assumed at 29,- 
 000,000 Ibs. In large sections of properly prepared material the 
 tensile elasticity probably averages a little over this, and the 
 compressive elasticity a little below it. 
 
 The following results of the tests for comparative elasticity in 
 tension and compression, will serve to illustrate the irregularity 
 of the elasticity ; also, see tests of iron and steel cut from beams, 
 given hereafter. 
 
20 
 
 WROUGHT IRON AND STEEL. 
 
 Two pieces of 3-inch square iron cut from same bar. 
 Measured length of each specimen = 12 inches. 
 Area of each specimen = .556 square inch. 
 Pressures in Ibs. ; change of length in inches. 
 
 TENSILE TEST. 
 
 COMPRESSIVE TEST. 
 
 
 Elongations. 
 
 
 Bednction of length. 
 
 Pressure per 
 sq. inch. 
 
 Load on. 
 
 Load off. 
 
 Pressure per 
 sq. inch. 
 
 Load on. 
 
 Load off. 
 
 5,000 
 
 .002 
 
 .000 
 
 5,000 
 
 .002 
 
 .000 
 
 10,000 
 
 .0045 
 
 .000 
 
 10,000 
 
 .0035 
 
 .000 
 
 15,000 
 
 .0065 
 
 .000 
 
 15,000 
 
 .005 
 
 .000 
 
 20,000 
 
 .0085 
 
 .000 
 
 20,000 
 
 .006 
 
 .000 
 
 22,000 
 
 .010 
 
 .000 
 
 22,000 
 
 .007 
 
 .000 
 
 24,000 
 
 .0105 
 
 .000 
 
 24,000 
 
 .008 
 
 .000 
 
 26,000 
 
 .0115 
 
 .000 
 
 26,000 
 
 .009 
 
 .000 
 
 28,000 
 
 .012 
 
 .000 
 
 28,000 
 
 .0095 
 
 .000 
 
 30,000 
 
 .013 
 
 .000 
 
 30,000 
 
 .010 
 
 .000 
 
 32,000 
 
 .0135 
 
 .000 
 
 32,000 
 
 .011 
 
 .000 
 
 34,000 
 
 .0145 
 
 .000 
 
 34,000 
 
 .020 
 
 .0035 
 
 36,000 
 
 .0155 
 
 .001 
 
 36,000 
 
 .023 
 
 .0045 
 
 38,000 
 
 .1715 
 
 .1495 
 
 38,000 
 
 .027 
 
 .010 
 
 40,000 
 
 .3835 
 
 .3605 
 
 40,000 
 
 .107 
 
 .089 
 
 50,000 
 
 1.326 
 
 1.2945 
 
 50,000 
 
 .272 
 
 .246 
 
 53,820 
 
 3.093 
 
 
 60,000 
 
 .464 
 
 .435 
 
 
 
 
 70,000 
 
 .'671 
 
 ]639 
 
 Specimen broke with 53,820 
 
 80,000 
 
 .845 
 
 814 
 
 Ibs. per square inch. 
 
 90,000 
 
 1.074 
 
 1.042 
 
 Stretched 3.093 in 12 in. 
 
 
 
 
 2. 187 in 8 in. 
 
 Modulus of elasticity 
 
 " 27. 3 per cent, in 8 in. 
 
 = 35,300,000 Ibs. 
 
 Fractured area = .3364 
 
 Modulus of elasticity 
 
 = 27,420,000 Ibs. 
 
ELASTICITY OF EOLLED IRON. 
 
 21 
 
 Two pieces of ^-inch round iron cut from same bar. 
 Measured length of each specimen = 12 inches. 
 Area of each specimen = .449 square inch. 
 Pressure in Ibs. ; change of length in inches. 
 
 TENSILE TEST. 
 
 COMPRESSION TEST. 
 
 
 Elongations. 
 
 
 Reduction of length. 
 
 Pressure per 
 
 Load on. 
 
 Load off. 
 
 Pressure per 
 
 Load on. 
 
 Load off. 
 
 sq. inch. 
 
 
 
 sq. inch. 
 
 
 
 5,000 
 
 .002 
 
 .000 
 
 5,000 
 
 .002 
 
 .000 
 
 10,000 
 
 .004 
 
 .000 
 
 10,000 
 
 .005 
 
 .000 
 
 15,000 
 
 .OC6 
 
 .000 
 
 15,000. 
 
 .007 
 
 .000 
 
 20,000 
 
 .008 
 
 .000 
 
 20,000 
 
 .010 
 
 .000 
 
 2,1,000 
 
 .009 
 
 .000 
 
 2-J.OOO 
 
 .011 
 
 .001 
 
 24,003 
 
 .010 
 
 .000 
 
 24,000 
 
 .012 
 
 .002 
 
 26,000 
 
 .0105 
 
 .000 
 
 26,000 
 
 .013 
 
 .003 
 
 28,000 
 
 .011 
 
 .000 
 
 28,000 
 
 .015 
 
 .0045 
 
 30,000 
 
 .013 
 
 .000 
 
 30,000 
 
 .o-as 
 
 .0065 
 
 32,000 
 
 .014 
 
 .('00 
 
 32,000 
 
 .02-^5 
 
 .007 
 
 34,000 
 
 .015 
 
 .002 
 
 34.000 
 
 .0275 
 
 .009 
 
 30,000 
 
 .022 
 
 .007 
 
 36,000 
 
 .040 
 
 .019 
 
 38,000 
 
 .416 
 
 .399 
 
 38,000 
 
 .052 
 
 .036 
 
 40,000 
 
 .544 
 
 .52 3 
 
 40,000 
 
 .133 
 
 .114 
 
 50,000 
 
 1.740 
 
 1.707 
 
 50,000 
 
 .304 
 
 .283 
 
 51,600 
 
 2.468 
 
 
 
 60,000 
 
 .427 
 
 .402 
 
 
 70,000 
 
 .546 
 
 .521 
 
 Specimen broke with 51,600 
 
 80,000 
 
 .663 
 
 .635 
 
 Ibs. per square inch. 
 
 90,000 
 
 .773 
 
 .742 
 
 Stretched 2. 468 in 12 in. 
 
 100,000 
 
 .896 
 
 .862 
 
 1.81 in 8 in. 
 
 
 " 22. 6 per cent, in 8 in. 
 
 Modulus of elasticity 
 
 Fractured area = .297 sq. in. 
 
 Modulus of elasticity 
 
 = 29,400,000 Ibs. 
 
 =24,490,000 Ibs. 
 
22 
 
 WROUGHT IRON AND STEEL. 
 
 A series of tests was made on the United States Government 
 testing machine at Watertown Arsenal, on the full-sized bars, 
 of which the following is a condensed average. 
 
 TENSILE TESTS. 
 
 
 
 K d" 
 
 c . 
 
 gh 
 
 
 
 
 
 a 
 
 |* 
 
 "" o 
 
 ft 
 
 
 MODE OF MANU- 
 
 JS 
 
 Zo, 
 
 -^ 
 
 * gf 
 
 tSjf 
 
 
 o 
 c 
 
 VjD 
 
 o 
 
 85 . 
 
 ll 
 
 FACTURE. 
 
 
 g"" 1 
 
 ~ ^ 
 
 " C 
 
 a 
 
 
 p 
 
 '- S.S 
 
 5 
 
 ^<S 8 
 
 "o 
 
 
 1 
 
 B" 
 
 s 
 
 
 
 * 
 
 Single rolled. . 
 
 3x1 
 
 50,000 
 
 28,600 
 
 29 
 
 28,200,000 
 
 Double rolled. . 
 
 3x1 
 
 52,503 
 
 30,100 
 
 32 
 
 27,885,000 
 
 Single rolled . . 
 
 5xli 
 
 49,800 
 
 26, 100 
 
 21 
 
 27,930,000 
 
 Double rolled. . 
 
 5x11 
 
 51,000 
 
 27,200 
 
 28 
 
 28,920,000 
 
 The "single and double rolled " means the number of work- 
 ings from the puddled bar. 
 
 A number of experiments on large columns with the same 
 machine gave the following results, also the tensile results, 
 for the iron used in the construction of the columns. 
 
 
 ELASTIC LIMIT. 
 
 MODULUS OF 
 ELASTICITY. 
 
 Wrought iron in compression 
 Wrought iron in tension 
 
 27,500 
 31, GOO 
 
 29, COO, 000 
 9,100,000 
 
 
 
 
 The modulus of transverse elasticity as applied to our tables of 
 deflections is taken at 26,000,000 Ibs. It is a hypothetical quan- 
 tity, derived by means of formulae, which are given elsewhere, 
 and which assume that the resistances to tension and compression 
 are equal, and that the successive fibres of iron, from the neu- 
 
SHEARING AND TORSION. 23 
 
 tral axis outward act independently of each other, neither of 
 which statements are correct in fact. 
 
 It is probable that this modulus, with the same material, will 
 vary with each change of section, and possibly also with changes 
 of length, and conditions of load. 
 
 SHEARING. 
 
 Under the conditions that shearing stresses are usually applied 
 in structures, the shearing strength of wrought iron is about 
 eight-tenths of the tensile, viz., 40,000 Ibs. per square inch of 
 section. But when subjected to the action of properly prepared 
 cutting knives, the resistance to shearing is much less than this. 
 
 TORSION. 
 
 The resistance to twisting is proportional to the cube of the 
 diameter. When the shearing strength is known, the torsional 
 strength of any round shaft can be determined as follows : T = 
 1.57 sr 3 . r radius of shaft in inches, s shearing strength 
 in Ibs. per square inch. T = the torsional moment in inch Ibs., 
 or the force in Ibs. multiplied by the leverage in inches with 
 which it acts. 
 
 In practice, however, torsion is usually accompanied by bend- 
 ing stresses, which must be always considered when determining 
 the proportions of shafts. See article on Shafting, page 170. 
 
WROUGHT IRON AND STEEL. 
 
 STRUCTURAL STEEL. 
 
 The various grades of steel used in structures possess such an 
 extended range of physical properties that it is impossible to 
 present as definite a basis for strength, stiffness, etc., as can be 
 given for wrought iron. 
 
 The character of the material is largely determined by its 
 combination, in minute proportions, with various substances, the 
 most important of which is carbon. 
 
 As a general rule the greater the percentage of carbon in the 
 steel, the higher will be its tensile strength and the lower its 
 ductility. The following list exhibits the average tensile re- 
 sistances for steels having given proportions of carbon : 
 
 PERCENTAGE 
 or CARBON. 
 
 TENSILE STRENGTH IN POUNDS PER 
 SQUARE INCH. 
 
 DUCTILITY. 
 
 ULTIMATE 
 TENACITY. 
 
 ELASTIC LIMIT. 
 
 ULTIMATE ELONGA- 
 TION IN 8 INCHES. 
 
 .10 
 
 60000 
 
 36000 
 
 26 per cent. 
 
 .15 
 
 G6000 
 
 40000 
 
 24 
 
 .20 
 
 74000 
 
 45000 
 
 22 
 
 .25 
 
 82000 
 
 50000 
 
 20 
 
 .30 
 
 90000 
 
 55000 
 
 18 
 
 .35 
 
 100000 
 
 60000 
 
 16 
 
 .40 
 
 110000 
 
 65000 
 
 14 
 
 These figures, however, are only approximate, as much de- 
 pends on the quality of the steel, and also the extent to which 
 it has been worked in the rolling process. 
 
 The grades below .15 per cent, carbon are known conven- 
 tionally as " mild steels," owing to their high ductility and to 
 their possessing but very moderate hardening properties when 
 chilled in water from a red heat. 
 
STRUCTURAL STEEL. 25 
 
 The mild steel has also superior welding properties, as com- 
 pared with hard steel, and will endure higher heat without 
 injury. 
 
 Steel whose carbon ratio does not exceed . 10 per cent, should 
 be capable of doubling flat without fracture, when chilled in the 
 coldest water from a red heat. 
 
 Steel of .12 carbon should endure similar treatment when 
 chilled in water of 80 F. 
 
 When the carbon percentage is . 15 the steel should be capable 
 of bending at least 90, over a curve whose radius is three or 
 four times the thickness of the specimen operated upon, and 
 after being chilled from a red heat in water of 80 F. 
 
 Steel having .35 to .40 per cent, carbon, will usually harden 
 sufficiently to cut soft iron, and maintain an edge. 
 
 There is much variation from the aforesaid hardening proper- 
 ties in different qualities of steel, as much depends on the influ- 
 ence of other hardening agents besides carbon. 
 
 The modern tendency is to limit the use of steel for structural 
 purposes to the milder grades of the material. For steel in 
 steamships the United States Government specifies as follows : 
 " Steel to have an ultimate tensile strength of not less than 
 60,000 Ibs. per square inch, and a ductility of not less than 25 
 per cent, in 8 inches. The test piece to be heated to a cherry- 
 red and chilled in water at a temperature of 82 F. After this 
 it must be capable of bending double flat under the hammer 
 without cracking." It requires about .11 to .12 carbon steel to 
 endure this test. 
 
 ( ' Lloyd's " rules require the steel to have an^ultimate tenacity 
 of not less than 60,000, or not over 70,000 Ibs. per square inch, 
 with an elongation of at least 16 per cent, in 8 inches. This 
 steel, when heated to redness and chilled in water of 82 F., 
 must bend double without fracture around a curve of which the 
 diameter is not more than three times the thickness of the piece 
 tested. For a cold test without hardening, the material must be 
 capable of doubling flat and bending backward without fracture. 
 
 Angles and beams for ship-frames may have a tenacity of 
 74,000 Ibs., providing the bending tests are satisfactory, and the 
 welding property is unimpaired. It requires about .12 to .14 
 carbon steel to meet these specifications. 
 
WROUGHT IRON AND STEEL. 
 
 We have made numerous experiments on steel of several 
 grades and in various forms, but the resistance under stress is 
 so uncertain that a fair statement of its physical properties can- 
 not be satisfactorily given until an exhaustive series of experi- 
 ments has been made on material of definite composition. 
 
 We present the average results of experiments on the strength 
 and elasticity of " mild " and " hard" steel, also the compara- 
 tive resistance of these materials in the form of struts. The 
 " mild steel " had an average carbon ratio of .12 per cent., and 
 the " hard steel " an average carbon ratio of .36 per cent. The 
 average strength and elasticity of wrought iron is inserted for 
 the purpose of exhibiting the characteristics of the steel and 
 iron. As in the case of the steel, the several values given for 
 iron are the results of a few special experiments. 
 
 MATERIAL. 
 
 TENSILE STRENGTH IN 
 LBS. PER SQUARE INCH. 
 
 DUCTILITY. 
 
 MODULUS op 
 ELASTICITY IN 
 LBS. 
 
 ULTIMATE 
 TENACITY. 
 
 ELASTIC 
 LIMIT. 
 
 ELONGATION IN 
 8 INCHES. 
 
 Iron 
 
 51000 
 64000 
 100000 
 
 31000 
 39000 
 56700 
 
 19 per cent. 
 24 
 18 
 
 28400000 
 29300000 
 29280000 
 
 Mild steel.... 
 Hard steel 
 
 From the same material the following results for compression 
 were obtained. 
 
 COMPRESSIVE RESISTANCE. 
 
 MATERIAL. 
 
 ELASTIC LIMIT IN LBS. 
 PBR SQUARE INCH. 
 
 MODULUS OF 
 ELASTICITY. 
 
 Iron 
 
 29500 
 
 27090000 
 
 Mild steel 
 
 37400 
 
 24760000 
 
 Hard steel 
 
 55700 
 
 24570000 
 
 
 
 
STRUCTURAL STEEL. 
 
 27 
 
 TRANSVERSE STRENGTH. 
 
 A series of experiments was made on the transverse strength 
 and elasticity of round bars from 3 to 4 inches in diameter, and 
 flanged beams varying from 3 to 12 inches deep, and from 3 feet 
 to 20 feet in length. For the purpose of making a compact ex- 
 hibit of the resistance of beams of various lengths and cross sec- 
 tions, the results of the experiments were condensed to the 
 method of the ensuing table, in which 
 
 R = the modulus of maximum resistance. 
 
 JR V = the modulus of resistance at the elastic limit. 
 
 E the modulus of transverse elasticity. 
 
 _, -. bending moment x depth of beam 
 
 H or H\. n i 7^ * 
 
 2 x inertia 
 
 _ Weight x cube of length t 
 ~~ 48 x Inertia x deflection 
 
 The ultimate resistance was taken at that stage of the experi- 
 ment where increase of deflection occurred without increase of 
 load. 
 
 MATERIAL. 
 
 R 
 
 By. 
 
 E 
 
 Iron 
 
 44700 Ibs 
 
 31000 Ibs 
 
 27600000 Ibs. 
 
 Mild steel 
 
 52800 " 
 
 39500 " 
 
 2970000D " 
 
 Hard steel 
 
 80200 " 
 
 54500 " 
 
 27200000 " 
 
 
 
 
 
 As is well known, the elasticity of iron is so variable and 
 uncertain, that no definite value can be assigned to it except 
 by taking the averages of numerous experiments. Steel 
 possesses the same uncertain elasticity, especially under trans- 
 verse and compressive stresses. 
 
 The elastic moduli in tension varied from 27 to 33 millions of 
 
28 
 
 WROUGHT IRON AND STEEL. 
 
 pounds, in compression from 21 to 33 millions, and transversely 
 the modulus oJt' elasticity varied from 23 to 33 millions of 
 pounds. 
 
 It is probable that there is not much difference on the whole 
 between the transverse elasticity of iron and either grade of 
 steel; if any difference at all exists, the steel probably has the 
 advantage in stiffness, and the experiments indicate that the 
 mild steel, if anything, is stiffer than the hard steel, the reverse 
 of what is popularly supposed to be the case. 
 
 STEEL BEAMS. 
 
 The experiments demonstrate that the transverse resistance of 
 steel of different grades maintains a ratio practically uniform 
 with the tenacities of the different steels. Consequently when 
 steel of known tensile strength is used in beams, the absolute 
 strength of the beam may be obtained from our rules and tables 
 for iron by increasing the results in the proportion of the in- 
 creased tenacity of the particular steel used over that of iron. 
 The percentage of increase for good qualities of steel, will be 
 about as follows : 
 
 CARBON PERCENTAGE. 
 
 INCREASED STRENGTH OF STEEL OVER WROUGHT 
 IRON BEAMS. 
 
 .10 
 
 20 per cent . 
 
 .15 
 
 35 " 
 
 .20 
 
 50 " 
 
 .25 
 
 65 " 
 
 .30 
 
 80 " 
 
 The experiments do not show that steel of any grade is stiffer 
 under working loads than wrought iron. Therefore beams of 
 either steel or wrought iron having uniform lengths and cross 
 sections will deflect uniformly under equal loads, below the elas- 
 tic limit of wrought iron, and our tables of deflections for iron 
 beams as given hereafter, will apply also to steel. 
 
STRUCTURAL STEEL. 29 
 
 STEEL SHAFTING. 
 
 When absolute strength irrespective of stiffness is alone con- 
 sidered, steel probably possesses a torsional strength exceeding 
 that of iron about in the ratio of the respective tenacities of the 
 two metals. Therefore, when designing shafting under such 
 conditions, our formulas for iron shafting can be used, substitut- 
 ing a shearing resistance equal to f of the tensile strength 
 of the steel, in place of that given for iron in the article on 
 Shafting. But in the large majority of cases the usefulness of 
 shafting is determined by its transverse stiffness, irrespective of 
 its ultimate torsional strength. 
 
 As in this respect the advantage of steel over iron is very 
 questionable, it will be found necessary to use the same dimen- 
 sions of steel shafts as determined by our rules foi wrought iron. 
 
 STEEL STRUTS. 
 
 The experiments on direct compression prove that the elastic 
 limits of steel, as of iron, under stresses of tension and com- 
 pression, are about equal. 
 
 Consequently for the shortest struts, where failure results from 
 the effects of direct compression, the tensile resistances of steel 
 and iron serve as a comparative measure of the strut resistance 
 of the two materials. 
 
 But as the strut is increased in length, and failure results 
 from lateral flexure before the compressive limit of elasticity is 
 attained, then the transverse elasticity of the material becomes 
 a factor of increasing importance in determining the strut resist- 
 ance. 
 
 As in this respect the steel possesses little advantage, if any, 
 over iron, the tendency will be for struts of steel and iron as the 
 length is increased to approximate toward equality of resist- 
 ance. This equality with iron will be attained, first by the 
 mildest steel, and latest by the hardest steel. 
 
 The results of many experiments we have made seem to dem- 
 onstrate that this equality of strut resistance is practically 
 attained between iron and mild steel, when the ratio of length 
 to least radius of gyration of cross section is about 200 to 1. In 
 
30 WROUGHT IRON AND STEEL. 
 
 the case of the harder steels, practical equality of resistance 
 would probably be reached at some higher but unknown ratio of 
 length to section. 
 
 We give a table exhibiting the comparative resistances per 
 square inch of section for flat-ended struts of iron, mild steel, 
 and hard steel, and for further particulars of the subject refer 
 to the article on Struts, given hereafter. 
 
 It is quite probable that grades of steel intermediate between 
 those denoted in the table will offer intermediate resistance as 
 struts, in the ratio of their percentage of carbon, other elements 
 remaining the same. 
 
 SPECIFIC GRAVITY. 
 
 The specific gravity of steel and iron varies according to the 
 purity of the metal, and also to the degree of condensation im- 
 parted by the rolling process. 
 
 As a rule the mild steel has a higher specific gravity than 
 hard steel, and both are denser than iron. A number of tests 
 we have made for specific gravity show rolled bars of mild steel 
 to vary from 7.84 to 7.83, and hard steel from 7.81 to 7.85 
 specific gravity. Ordinary iron bars will vary from 7 . 6 to 7 . 8. 
 
 In the form of beams and large rolled sections generally, the 
 following figures may be accepted as a fair average. 
 
 Material. Weight, per cubic foot. Weight per cubic inch. 
 
 Mild Steel 489.0 Ibs. .283 Ib. 
 
 Hard Steel 486. G " .2815 " 
 
 Iron 478.3 " .2768 " 
 
 Or for the same sectional areas, the excess in weight over iron 
 will be, for mild steel 2.24 per cent, and for hard steel 1.7 per 
 per cent. 
 
STBUCTUEAL S 1 
 
 FLAT-ENDED ST 
 
 ULTIMATE RESISTANCE IX POUNDS PEK SQUARE INCH OF 
 SECTION. 
 
 UNIVERSITY 
 
 LENGTH DIVIDED 
 BY LEAST RADIUS 
 OF GYRATION. 
 
 IRON. 
 
 MILD STEEL. 
 .12 CARBON. 
 
 HARD STEEL. 
 .36 CARBON. 
 
 20 
 
 46000 
 
 70000 
 
 100000 
 
 30 
 
 43000 
 
 51000 
 
 74000 
 
 40 
 
 40000 
 
 46000 
 
 62000 
 
 50 
 
 38000 
 
 44000 
 
 60000 
 
 60 
 
 36000 
 
 42000 
 
 58000 
 
 70 
 
 31000 
 
 40000 
 
 55500 
 
 80 
 
 32000 
 
 38000 
 
 53000 
 
 90 
 
 30900 
 
 36000 
 
 49700 
 
 100 
 
 '29800 
 
 34000 
 
 46500 
 
 110 
 
 28000 
 
 3200J 
 
 43200 
 
 120 
 
 26300 
 
 30000 
 
 40000 
 
 180 
 
 24900 
 
 2doco 
 
 36700 
 
 140 
 
 23500 
 
 26000 
 
 33500 
 
 150 
 
 21750 
 
 24000 
 
 30700 
 
 160 
 
 20000 
 
 220DO 
 
 28000 
 
 170 
 
 18400 
 
 20000 
 
 25500 
 
 180 
 
 16800 
 
 18000 
 
 23000 
 
 190 
 
 15850 
 
 1U300 
 
 2101)0 
 
 200 
 
 14500 
 
 14800 
 
 19000 
 
 210 
 
 13600 
 
 13600 
 
 17200 
 
 220 
 
 12700 
 
 12700 
 
 15500 
 
 230 
 
 11950 
 
 11950 
 
 14400 
 
 240 
 
 11200 
 
 11200 
 
 13400 
 
 250 
 
 10500 
 
 10500 
 
 12400 
 
 260 
 
 98 
 
 9800 
 
 11500 
 
 270 
 
 9150 
 
 9150 
 
 10600 
 
 280 
 
 8500 
 
 8500 
 
 9700 
 
 290 
 
 7850 
 
 7850 
 
 9000 
 
 300 
 
 7200 
 
 7200 
 
 8500 
 
32 WROUGHT IRON AND STEEL. 
 
 RESISTANCE TO BENDING. 
 
 When wrought-iron beams are subjected to bending stresses, 
 the resulting deflections increase nearly in direct proportion to 
 the increase of load, up to the limit of elasticity of the iron. 
 Slight permanent sets can be observed in the beam before the 
 elastic limit is reached, just as similar sets are obtained in longi- 
 tudinal tests. After the elastic limit is passed, the deflections 
 increase in a greater ratio than the loads, and clearly defined 
 permanent sets occur, until another stage in the experiment is 
 reached, when the beam shows increasing deflection without any 
 increase of load. At this point the element of time becomes an 
 important factor. The load can be very slowly increased, with- 
 out the record of stress showing increase, but if the load is freely 
 applied, the recorded stress may be very considerably augmented. 
 It is probable that if the load was left long enough on the beam 
 at this stage of the experiment entire failure would ensue. 
 
 We call this point, which can generally be very clearly ob- 
 served, the "ultimate resistance " of the beams, and whenever 
 such terms as "ultimate load," " breaking load," etc., are used 
 in connection with bending stresses, this is the load referred to. 
 The stress at the elastic limit bears no such fixed relation to the 
 ultimate stress as can generally be observed in tensile tests. 
 The length of the beam, and probably other conditions, such as 
 position of load, etc., become factors in determining the ratio, 
 which in the absence of complete experiments cannot be decided. 
 
 MODULUS OF RUPTURE. 
 
 If the material of a beam offered equal resistances to tension 
 and compression, and if the fibres acted independently of each 
 other in effecting this resistance, then the maximum fibre stresses, 
 which occur at the top and bottom of the beam, could be readily 
 calculated as follows: 
 
 For any rectangular section loaded in the middle S = 5-^-71 ', 
 
 o d 
 
 for a beam 1 inch square and 12 inches long, S = 18 W, or in 
 general terms for any symmetrical beam, under any condition of 
 
LIMITS FOR THE SAFE LOAD. 33 
 
 8 = maximum fibre stress. w = load. 
 
 6 = breadth of beam. I = length of beam. 
 
 d = depth of beam. M bending moment. 
 
 / = moment of inertia about the neutral axis at right angles to 
 the direction of pressure. 
 
 But, as previously stated, neither of these usually assumed 
 conditions exist. 
 
 It seems probable that the fibres nearer the axis, by means of 
 lateral adhesion, relieve the outer fibres from a portion of the 
 stress which the usually accepted theory indicates, and conse- 
 quently have their own portion of the theoretical stress cor- 
 respondingly increased. It is therefore necessary to abandon the 
 deceptive term of "maximum fibre stress," and substitute a 
 " modulus " determined by means of the foregoing formulae. 
 
 This modulus will vary for varying cross-sections, and recent 
 experiments make it seem probable that it will vary with the 
 length of beam, etc. 
 
 The average of a large number of experiments on standard 
 flanged beams give an ultimate modulus of 42,000 Ibs. On solid 
 rectangular sections the modulus will run higher, or from 45,000 
 to 50,000 Ibs. 
 
 We adopt 42,000 as the modulus for ultimate transverse 
 strength of I beams. All our tables are calculated by taking 
 S 14,000, or one-third of the ultimate strength of the beam. 
 
 LIMITS FOR THE SAFE LOAD. 
 
 Inasmuch as there is a great diversity in published tables of 
 safe loads for beams, every one must judge for himself what pro- 
 portion of the elastic strength of the beam will best suit his 
 purpose. 
 
 The character of the load must be considered, and the mode of 
 application of the same. If the load is suddenly applied, espe- 
 cially if accompanied by impact, the dynamic stresses resulting 
 therefrom will not be expressed by fcrmulae which are derived 
 from static considerations alone. Freedom from vibration or 
 excessive deflection have usually to be provided for, or the beam 
 may be of considerable length without lateral support. In many 
 such cases it may be necessary to take one-fourth or one-fifth of 
 the ultimate strength of the beam as the working basis, instead of 
 3 
 
34: WROUGHT IRON AND STEEL. 
 
 one-third, as given in our tables, which we give as the " great- 
 est safe loads." 
 
 We have every confidence in the accuracy of the tables, as the 
 results of a number of careful tests we have recently made show 
 that very rarely does the ultimate strength of the beam fall below 
 the limits we have given, and in some instances it considerably 
 exceeds those limits. 
 
 We have in our own service beams that are continually subjected 
 to much higher bending stresses than would be assigned to them 
 by our tables without any evidence of a want of stability. 
 
 FACTOR OF SAFETY. 
 
 For factors of safety the following table will give results in 
 harmony with good practice. 
 
 CHARACTER OF STRESS. GREATEST SAFE LOAD. 
 
 Quiescent load, subject to little or no vibra- [ .1. o ultimate 
 tion as in light roofs, etc. J 
 
 Fluctuating loads causing vibration, but") 
 
 no sudden application of the maximum I , -,,. , 
 load. Such as lateral bracing of bridges, f * ol 
 roofs carrying shafting, etc. J 
 
 When maximum loads are suddenly ap- 
 plied. 
 
 When maximum stresses are suddenly re- ) t . 
 versed in direction. f oi 
 
 UNSYMMETRICAL BEAMS. 
 
 When beams have not an identical cross-section above and 
 below the neutral axis, as in Deck Beams, Tees, Angles, etc., 
 experiment shows no substantial difference in either the strength 
 or stiffness of the beams, whether the greatest flange is in ten- 
 sion or compression, up to or nearly to the elastic limit. When 
 the least flange is in compression the elastic limit ranges a little 
 higher than when it is in tension, and in the former case, after 
 the elastic limit is passed, the beam generally exhibits much less 
 deflection and higher ultimate resistance than when loaded with 
 
PENCOYD BEAMS GREATEST SAFE LOAD. 35 
 
 the least flange in tension. This is probably due to the high 
 resistance of wrought iron to crushing after the elastic limit is 
 
 There are some exceptions to this, as in the case of very long 
 beams that present no adequate resistance to lateral flexure, but 
 as such cases are outside the bounds of good practice they re- 
 quire no further notice. The authoritative formula? most gener- 
 ally accepted are based upon a maximum fibre stress obtained as 
 
 follows: S=-j-' -3f= bending moment, d = distance from 
 
 neutral axis to farthest edge of section. I = moment of inertia 
 about the axis passing through the centre of gravity at right 
 angles to direction of pressure. This does not give results in 
 harmony with experiments, except by taking S as a modulus, 
 whose value would not agree with that used for symmetrical 
 beams, and whose value would have to be derived by experiments 
 for differing cross-sections. By taking the moments of inertia 
 above and below an axis so located that the forces producing 
 tension and compression are in equilibrium, and using the mod- 
 ulus, S 42,000, as in symmetrical beams, results harmonizing 
 with experiments are obtained. 
 
 But, for simplicity, we have adopted the following methods 
 for calculating the safe load, which, though incorrect in prin- 
 ciple, yet give correct results for the particular sections referred 
 to. 
 
 Deck Beams -g-j = S = 42,000. 
 
 Tees and Angles of equal legs and ) f*_4 _ 45 000. 
 uniform thickness. f 2 / 
 
 Notation as for equal flanged beams. 
 
 PENCOYD BEAMS. 
 
 GREATEST SAFE LOADS. 
 
 The following tables for I beams, channels, and deck beams 
 give the greatest safe loads in net tons, evenly distributed over 
 the beams, and including the weight of beam itself. 
 
 These loads are one-third () of the ultimate strength of the 
 beams, and are correct for the corresponding sectional areas 
 
36 
 
 WKOUGHT IKON AND STEEL. 
 
 given. The several values are obtained by the methods described 
 on page 88, and have been confirmed by numerous experi- 
 ments. The beams, if of considerable length, are supposed to 
 be braced horizontally, and it is safest to limit the application of 
 the tabular loads to beams whose length between lateral sup- 
 ports does not exceed twenty times the flange width. 
 
 Our experience has been that a beam without lateral support 
 is much more stable than is commonly supposed. In an open 
 webbed beam, the top flange acts as a simple strut, and is liable 
 to lateral flexure when the unsupported length is considerable. 
 But in a solid beam the parts in tension sustain the parts in com- 
 pression rigidly, and prevent the buckling which would other- 
 wise occur. 
 
 A number of careful experiments have shown a reduction of 
 about one-third of the normal modulus of rupture when the 
 length of the beam becomes 80 times its flange width. But as 
 the long beam may suffer if exposed to accidental cross strains, 
 we recommend the greatest safe load to be reduced in such a 
 ratio for long beams that when the length is seventy times the 
 flange width the greatest safe loads will be reduced one-half. 
 This will give safe loads, corresponding to given lengths as fol- 
 lows: 
 
 BEAMS WITHOUT LATERAL SUPPORT. 
 
 LENGTH OF BEAM. 
 
 PROPORTION OP TABULAR LOAD FORMING 
 GREATEST SAFE LOAD. 
 
 20 times flange width. 
 
 30 " 
 40 
 
 50 " " " 
 GO " 
 
 70 ' 
 
 Whole tabular load. 
 
 rfc 
 
 
 
 The safe loads for any other length, not given in the tables 
 
DEFLECTION. 37 
 
 can readily be found by simple proportion, remembering if the 
 span is very short to limit the load to that given in col. xiv, 
 pages 93-97, headed " Maximum load in tons." If beams of any 
 sectional area not given in the tables are used, the strength can 
 be found as described on page 106, or a close approximation to 
 the same by the rule on page 69. 
 
 DEFLECTION". 
 
 Inasmuch as the elasticity of iron and steel is very variable 
 and uncertain, the tabular deflections are given as the nearest 
 probable, and are obtained as described on page 89. 
 
 The tabular deflections correspond to the given loads evenly 
 distributed, and apply to any sectional area for each size of 
 beams respectively, when the corresponding loads bear a uni- 
 form ratio to the strength of the beam. 
 
 The greatest safe load in the middle of the beam is exactly 
 one-half (i) of the distributed load, and the deflection for the 
 former will be eight-tenths (y,,) of the deflection corresponding 
 to the distributed load as given in the tables. If the load is 
 placed out of centre on the beam, it will bear the same ratio to 
 the load at the centre that the square of half the span bears to 
 the product of the segments of the beam formed by the position 
 of the load. 
 
 Example. A 15-inch 200 Ib. I beam, 16 feet between sup- 
 ports, will safely carry an evenly distributed load (by the tables) 
 of 26.5 tons, and deflect under same .27 inches. The greatest 
 safe load in the middle will be one-half the above, viz., 13.25 
 tons, and the resulting deflection fa of the former, or .22 
 inches. 
 
 If the weight is concentrated 3 feet out of centre, or 5 feet 
 and 11 feet from the ends, then the square of half the span being 
 64, and the product of the segments being 55, the greatest safe 
 
 , , .,. , 18.25x64 
 
 load will be = 15.4 tons. 
 
 55 
 
 If a beam of above size and length is used without any lateral 
 support, reduce the safe load in the ratio aforesaid. Thus the 
 flange is 5$ inches wide, and the length 33 times this ; there- 
 fore the greatest safe load will be a little less than & of the 
 results in the example. 
 
OS WROUGHT IRON AND STEEL. 
 
 If the beam is exposed to much vibration, or the action of 
 moving loads, etc. , reduce the tabular loads, as previously de- 
 scribed on page 34. 
 
 For beams of other character than described, the greatest 
 safe loads and corresponding deflections will bear the following 
 ratios to the tabulated loads, for the same lengths of beams : 
 
 CHARACTER OP BEAM. 
 
 GREATEST SAFE LOAD. 
 
 DEFLECTION. 
 
 Fixed at one end, with the 
 load concentrated at the 
 other end. 
 
 One-eighth (*-) part 
 of the tabular 
 load. 
 
 Three and one- 
 fifth (8Jl) times 
 the tabular de- 
 flection. 
 
 Fixed at one end, with the 
 load uniformly distrib- 
 uted. 
 
 One-fourth ({) part 
 of the tabular 
 load. 
 
 Two and two- 
 fifths (2|)times 
 the tabular de- 
 flection. 
 
 Rigidly fixed at both ends, 
 with a load in the mid- 
 dle of beam. 
 
 Same as the tabu- 
 lar load. 
 
 Four-tenths (-&) 
 of the tabular 
 deflection. 
 
 Rigidly fixed at both ends, 
 with the load uniformly 
 distributed. 
 
 One and one-half 
 (li) times the 
 tabular load. 
 
 One-sixth () of 
 the tabular de- 
 flection. 
 
 Continuous beam loaded in 
 middle. 
 
 Same as the tabu- 
 lar load. 
 
 Four-tenths (-&) 
 of the tabular 
 deflection. 
 
 Continuous beam load uni- 
 formly distributed. 
 
 One and one half 
 (H) times the 
 tabular load. 
 
 One-sixth () of 
 the tabular de- 
 flection. 
 
LIMIT FOB DEFLECTION. 39 
 
 BEAMS WITH FIXED ENDS. 
 
 It is necessary to bear in mind the distinction between ends 
 "rigidly fixed" and ends simply "supported," the latter being 
 the class contemplated in all our tables of safe loads. By 
 "rigidly fixed," as denoted in the previous table, we mean that 
 the beam must be so securely fastened at both ends, by being 
 built into solid masonry, or so firmly attached to au adjacent 
 structure, that the connection would not be severed if the beam 
 was exposed to its ultimate load. In this case, the beam is of 
 the same character as if continuous over several supports, or 
 as if consisting of two cantilevers, the space between whose 
 ends was spanned by a separate beam. 
 
 CONTINUOUS BEAMS. 
 
 If a beam is continuous over several supports, and is equally 
 loaded on each span, the greatest safe loads and the resulting 
 deflections on any intermediate span will be as given in the pre- 
 ceding table. But the end spans of such a beam, being only 
 semi-continuous, must be either of a shorter span than the in- 
 termediates, or if of the same length, the load must be dimin- 
 ished. See ''Continuous Beams," page 75. 
 
 LIMIT FOR DEFLECTION. 
 
 It is considered good practice in the case of plastered ceilings, 
 or in other circumstances where undue deflection may be pre- 
 judicial, to proportion beams so that their deflection will not ex- 
 ceed g l - of an inch per foot of span, or - 3 - n - part of the span. 
 A heavy black line is marked across, or partly across, each page. 
 All beams below these lines will deflect in excess of this limit; 
 those above the line are safe to use. 
 
40 
 
 WROUGHT IKON AND STEEL. 
 
 15" 
 
 PENCOYD 
 
 BEAMS. 
 
 12" 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of beam. 
 For a load in middle of beam, allow one-half the tabular figures. 
 Deflection for latter load will be -fa of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 
 
 1 
 
 2 
 
 2 
 
 go 
 
 - 
 
 3 
 
 3 
 
 4 
 
 4 
 
 
 
 i 
 
 SIZE OF BEAM 
 IN INCHES. 
 
 15" 
 
 15" 
 
 15" 
 
 15" 
 
 M 
 
 12" 
 
 12" 
 
 12" 
 
 12" 
 
 |t 
 
 WT. PER YD. 
 IN LBS. 
 
 233 
 
 200 
 
 201 
 
 145 
 
 I 
 
 1&4 
 
 168 
 
 163 
 
 120 
 
 I 
 
 MOMENT OF 
 INERTIA. 
 
 743.6 
 
 682.1 
 
 626.6 
 
 521.2 
 
 | 
 
 403.5 
 
 372.0 
 
 324.6 
 
 272.9 
 
 | 
 
 
 GREATEST SAFE LOAD. 
 
 H 
 
 P 
 
 GREATEST SAFE LOAD. 
 
 P 
 
 10 
 
 46.29 
 
 42.44 
 
 38.96 22.10 
 
 11 
 
 31.36 28.93 
 
 25.24 
 
 21.22 
 
 .13 
 
 11 
 
 42.08 
 
 38.58 
 
 35.42 22.10 
 
 13 
 
 28.51 26.30 22.95 
 
 19.29 
 
 .16 
 
 12 
 
 38.57 
 
 35.37 
 
 32.47 22.10 
 
 IB 
 
 26.13 24.11 
 
 21.03 
 
 17.69 .19 
 
 13 
 
 35.61 
 
 32.65 
 
 29.97 
 
 22. 10 
 
 .18 
 
 24.12 
 
 22.25 
 
 19.42 
 
 16.32 
 
 .22 
 
 14 
 
 33.06 
 
 30.31 
 
 27.83 
 
 22.10 
 
 21 
 
 22.40 
 
 20.67 
 
 18.03 
 
 15.16 
 
 .26 
 
 EH 15 
 
 30.815 
 
 28.29 
 
 5>5.97j 21.62 
 
 ?4 
 
 20.91 19.29 
 
 16.83 
 
 14.15 
 
 .30 
 
 W 16 
 
 28.93 
 
 26.53 
 
 21.35 
 
 20. -27 
 
 27 
 
 19.60 18.08 
 
 15.76 
 
 13.26 .34 
 
 g 17 
 
 27.23 
 
 24.96 
 
 22.92 
 
 19.08 
 
 .30 
 
 18.45 
 
 17.02 
 
 14.85 
 
 12.48 
 
 .38 
 
 ^ 18 
 
 25.72 
 
 23.58 
 
 21.64 
 
 18.02 
 
 34 
 
 17.42 
 
 16.07 
 
 14.02 
 
 11.79 
 
 .43 
 
 K 19 
 
 24.36 
 
 22.34 
 
 20.51 
 
 17.07 
 
 38 
 
 16.51 
 
 15.23 
 
 13.28 
 
 11.17 
 
 .48 
 
 20 
 
 23.14 
 
 21.22 
 
 19.48 
 
 16.21 
 
 42 
 
 15.68 
 
 14.47 
 
 12.62 
 
 10.61 .53 
 
 21 
 
 22.04 
 
 20.21 
 
 18.55 
 
 15.44 
 
 .46 
 
 14.93 
 
 13.78 
 
 12.02 
 
 10.11 .58 
 
 OQ 22 
 
 21.04 
 
 19.29 
 
 17.71 
 
 14.74 
 
 .51 
 
 14.25 
 
 13.15 
 
 11.47 
 
 9.65 
 
 4 
 
 23 
 
 20.13 
 
 18.45 
 
 16.94 
 
 14.10 
 
 .56 
 
 13.63 
 
 12.58 
 
 10.97 
 
 9.23 
 
 .70 
 
 &H 24 
 
 19.29 
 
 17.68 
 
 16.23 
 
 13.51 
 
 .61 
 
 13.07 
 
 12.05 
 
 10.52 
 
 8.84 .77 
 
 25 
 
 18.52 
 
 16.98 
 
 15.58 
 
 12.97 
 
 .66 
 
 12.54 
 
 11.57 
 
 10.10 
 
 _8J9L83 
 
 g 36 
 g 27 
 
 17.80 
 17.14 
 
 16.32 
 15.72 
 
 14.99 
 14.43 
 
 12.47 
 12.01 
 
 .72 
 
 77 
 
 12.06 
 11.61 
 
 11.13 
 10.72 
 
 9.71 
 9.35 
 
 8.16 .90 
 7.86 .97 
 
 H 28 
 
 16.53 
 
 15.16 
 
 13.91 
 
 11.58 
 
 83 
 
 11.20 
 
 10.33 
 
 9.01 
 
 7.581.05 
 
 S 29 
 
 15.96 
 
 14.63 
 
 13.43 
 
 11.18 
 
 .89 
 
 10.81 
 
 9.98 
 
 8.70 
 
 7.32 
 
 1.12 
 
 30 
 
 15.43 
 
 14.15 
 
 12.99 
 
 10.81 
 
 95 
 
 10.45 
 
 9.64 
 
 8.41 
 
 7.07 
 
 1.20 
 
 31 
 
 14.93 13.69 
 
 12 57i 10.46 
 
 1 0?, 
 
 10.12 
 
 9.33 
 
 8.14 
 
 6.85 
 
 1.28 
 
 32 
 
 14.47 13^6 
 
 ira 
 
 10.13 
 
 l"09 
 
 9.80 
 
 9.04 
 
 7.89 
 
 6.63 
 
 1.36 
 
 33 
 
 14.03 12.86 
 
 11.81 
 
 9.83 
 
 1.16 
 
 9.50 
 
 8.76J 7.65 
 
 6.43 
 
 1.44 
 
TABLE OF SAFE LOADS. 
 
 41 
 
 PENCOYD 
 
 101" 
 
 BEAMS. 
 
 10" 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of beam. 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be y - of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 5 
 
 5 
 
 E* 
 
 5t 
 
 6 
 
 6 
 
 GC 
 
 7 
 
 7 
 
 8 
 
 8 
 
 
 
 
 
 
 
 
 
 
 H 
 
 
 
 
 
 1 
 
 SIZE OF 
 
 
 
 
 
 
 
 
 
 
 
 BEAM IN 
 
 iot" 
 
 iot" 
 
 ict" 
 
 ict" 
 
 iot" 
 
 ict" 
 
 < 
 
 10" 
 
 10" 
 
 10" 
 
 10" 
 
 
 INCHES. 
 
 
 
 
 
 
 
 
 
 1-1 
 
 
 
 
 
 o 
 
 WT. PER 
 
 
 
 
 
 
 
 
 
 
 
 
 M 
 
 YARD IN 
 
 161 
 
 134 
 
 135 
 
 108 
 
 109 
 
 89 
 
 
 
 137 
 
 112 
 
 106 
 
 90 
 
 
 
 LBS. 
 
 
 
 
 
 
 
 fc 
 
 
 
 
 
 92 
 
 MOMENT 
 
 
 
 1 ! 
 
 
 fc 
 
 
 
 
 
 
 OF 
 
 265.7 
 
 241.6 
 
 219.5 
 
 195.4 
 
 180.3 
 
 162.3 
 
 
 
 194.4 173.6 
 
 161.3 
 
 148.3 
 
 
 
 INERTIA. 
 
 
 
 
 
 
 
 H 
 
 
 
 
 H 
 
 
 GREATEST SAFE LOAD. 
 
 W 
 fi 
 
 GREATEST SAFE LOAD 
 
 1 
 
 10 
 
 23.62 
 
 21.49 
 
 19.51 
 
 17.37 16.03 
 
 13.35 
 
 .15 
 
 18.14 
 
 16.20 
 
 15.08 
 
 13.84 
 
 .16 
 
 11 
 
 21.47 
 
 19.54 
 
 17.74 
 
 15.79 14.57 
 
 13.11 
 
 .18 
 
 16.49 14.73 
 
 13.71 
 
 12.58 
 
 .19 
 
 12 
 
 19.68 
 
 17.91 
 
 16.26 
 
 14.48 13.3H 
 
 12.02 
 
 .22 
 
 16.13118.50 
 
 12.57 
 
 11.54 
 
 .23 
 
 13 
 
 18.17 
 
 16.53 
 
 15.01 
 
 13.36 12.33 
 
 11 09 
 
 23 
 
 13 95 12 46 
 
 11.60 
 
 10.65 
 
 .27 
 
 14 
 
 16.87 
 
 15.35 
 
 13.94 
 
 12.41 
 
 11.4-) 
 
 10.30 
 
 .30 
 
 12.94 
 
 11.57 
 
 10.77 
 
 9.89 
 
 .3] 
 
 15 
 
 15.75 
 
 14.33 
 
 13.01 
 
 11.58 
 
 10.69 
 
 9.61 
 
 .34 
 
 12.0910.80 
 
 JO. 05 
 
 9.23 
 
 .36 
 
 H 16 
 
 14.76 
 
 13.43 
 
 12.19 
 
 10.86 
 
 10.02 
 
 9.01 
 
 .39 
 
 11.34 10.13 
 
 9.42 
 
 8.65 
 
 .41 
 
 
 13.90 
 
 12.64 
 
 11.48 
 
 10.22 
 
 9.43 
 
 8.48 
 
 .44 
 
 10.67 
 
 9.53 
 
 8. 87 
 
 8.14 
 
 .46 
 
 ^ 18 
 
 13.12 
 
 11.94 
 
 10.84 
 
 9.65 
 
 8.91 
 
 8.01 
 
 .49 
 
 10.08 
 
 9.00 
 
 8.38 
 
 7.fi9 
 
 .52 
 
 19 
 
 12.43 
 
 11.31 
 
 10.27 
 
 9.14 
 
 8.44 
 
 7.59 
 
 .55 
 
 9.55! 8.53 
 
 7.94 
 
 7.29 
 
 .58 
 
 H 20 
 
 11 81 
 
 10.74 
 
 9.75 
 
 8.69 
 
 8.01 
 
 7.21 
 
 .61 
 
 9.071 8.10 
 
 7.E4 
 
 6.92 
 
 .64 
 
 21 
 
 J1.25 
 
 10.23 
 
 9.29 
 
 8.27 
 
 7.63 
 
 6.87 
 
 .6*! 
 
 Tel 
 
 T72 
 
 TTs 
 
 T^"S 
 
 
 On 
 
 MataMi 
 
 
 mean** t ^ 
 1 
 
 """" 
 
 
 " 
 
 
 
 
 
 
 M 22 
 
 10.74 
 
 9.77 
 
 8.87 7.90 
 
 7.28 
 
 6.55 
 
 .74 
 
 8.25 
 
 7.36 
 
 6.85 
 
 6.29 
 
 .78 
 
 & 23 
 
 10.27 
 
 9.34 
 
 8.48 7.55 6.97 
 
 6.27 
 
 .81 
 
 7.89 
 
 7.04! 6.56 
 
 6.02 
 
 .85 
 
 24 
 
 9.84 
 
 8.95 
 
 8.13 7.24 6. 68 
 
 6.01 
 
 .83 
 
 7.56 
 
 6.75! 6.28 
 
 5.77 
 
 .92 
 
 K 25 
 
 9.45 
 
 8.60 
 
 7.80 
 
 6.95 6.41 
 
 5.77 
 
 .95 
 
 7.26 
 
 6.48 
 
 6.03 
 
 5.54 
 
 1.00 
 
 H 
 
 
 
 
 
 
 
 
 
 
 
 
 < 26 
 
 9 00 
 
 8 27 
 
 7 51 
 
 6 6*3 fi 16 
 
 5 54 
 
 1 03 
 
 6 98 
 
 6 23 
 
 5 80 
 
 5 32 
 
 1 08 
 
 
 8.75 
 
 7.96 
 
 7.23 6.43 5.94 
 
 5.34 
 
 1.11 
 
 6.72 
 
 6.00! 5.59 
 
 5.13 
 
 1.17 
 
 3 28 
 
 8.43 
 
 7.67 
 
 6.97 6.20 5.72 
 
 5.15 
 
 1.19 
 
 tf.48 
 
 5.79 5.39 
 
 4.94 
 
 1.26 
 
 29 
 
 8.14 
 
 7.41 
 
 6.73 
 
 5.99 5.53 
 
 4.97 
 
 1.28 
 
 6.26 
 
 5. 59 5.20 
 
 4.77 
 
 1.35 
 
 30 
 
 7.87 
 
 7.17 
 
 6.51 
 
 5.79 5.34 
 
 4.80 
 
 1.37 
 
 6.05 
 
 5.40 5.03 
 
 4.61 
 
 1.44 
 
 31 
 
 7 6" 
 
 6 93 
 
 6 29 5 60 5 16 
 
 4.65 
 
 1 46 
 
 5 85 
 
 5 23 4 86 1 4 47 
 
 1 54 
 
 32 
 
 7.38 
 
 6.72 
 
 6.09 5.43 5.01 
 
 4.50 
 
 1.57 
 
 5.67 
 
 5.061 4.71 
 
 4.33 
 
 1.64 
 
 33 
 
 7.19 
 
 6.51 
 
 5.91 
 
 5.26 4.86 
 
 4.37 
 
 1.68 
 
 5.50 
 
 4.91 
 
 4.57 
 
 4.19 
 
 1.75 
 
WROUGHT IRON AND STEEL. 
 9" 
 
 PENCOYD 
 
 8" 
 
 BEAMS. 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 
 Deflection in incites corresponding to given loads for each size of beam. 
 
 For load in middle allow one-half the tabular figures. 
 
 Deflection for latter load will be -jjo of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 9 
 
 9 
 
 10 
 
 10 
 
 W 
 
 11 
 
 11 
 
 12 
 
 12 
 
 * 
 
 
 
 
 
 
 M 
 
 
 
 
 
 < 
 
 SIZE OF BEAM 
 IN INCHES. 
 
 9" 
 
 9" 
 
 9" 
 
 9" 
 
 B 
 
 8" 
 
 8" 
 
 8" 
 
 8" 
 
 S> 
 
 WT. PER YD. 
 IN LBS. 
 
 122 
 
 90 
 
 QQ 
 
 70 
 
 C- 
 
 g 
 
 00 
 
 109 
 
 81 
 
 75 
 
 65 
 
 1 
 
 MOMENT OF 
 INERTIA. 
 
 143.7 
 
 118.8 
 
 106.8 
 
 94.4 
 
 o 
 
 98.6 
 
 3.9 
 
 74.5 
 
 09.2 
 
 1 
 
 
 GREATEST SAFE LOAD. 
 
 c 
 
 p 
 
 GREATEST SAFE LOAP. 
 
 1 
 
 6 
 
 24.27 
 
 16.53 
 
 18.42 
 
 9.94 
 
 .06 
 
 19.22 15.49 
 
 14.48 
 
 10.46 
 
 .07 
 
 7 
 
 20.80 
 
 16.53 
 
 15.79 
 
 9.94 
 
 .08 
 
 16.47; 13.99 
 
 12.41 
 
 10.46 
 
 .10 
 
 8 
 
 18.20 
 
 15.40 
 
 13.81 
 
 9.94 
 
 .11 
 
 14.41 12.24 
 
 10.86 
 
 10.08 
 
 .13 
 
 9 
 
 10.18 
 
 13.69 
 
 12.27 
 
 9.94 
 
 .14 
 
 12.81 
 
 10.88 
 
 9.66 
 
 8.96 
 
 .16 
 
 10 
 
 14.56 
 
 12.32 
 
 11.05 
 
 9.79 
 
 .18 
 
 11.53 
 
 9.79 
 
 8.69 
 
 8.07 
 
 .20 
 
 EH 11 
 
 13.24 
 
 11.20 
 
 10.04 
 
 8.90 
 
 .22 
 
 10.48 8.90 
 
 7.90 
 
 7.33 
 
 .24 
 
 W 12 
 
 12.13 
 
 10.26 
 
 9.21 
 
 8.16 
 
 .26 
 
 9.61 
 
 8.16 
 
 7.24 
 
 6.72 
 
 .29 
 
 g 13 
 
 11.20 
 
 9.48 
 
 8.50 
 
 7.53 
 
 .30 
 
 8.8? 
 
 7.53 
 
 6.68 
 
 6.21 
 
 .34 
 
 *r 14 
 
 10.40 
 
 8.80 
 
 7.89 
 
 7.00 
 
 .35 
 
 8.24 
 
 6.99 
 
 6.21 
 
 5.76 
 
 .39 
 
 G 15 
 
 9.71 
 
 8.21 
 
 7.37 
 
 6.53 
 
 .40 
 
 7.69 
 
 6.53 
 
 5.79 
 
 5.38 .45 
 
 16 
 
 9.10 
 
 7.70 
 
 6.91 
 
 6.12 
 
 .46 
 
 7.21 
 
 6.12 
 
 5.43 
 
 5.04 .51 
 
 5j 17 
 
 8.56 
 
 7.25 
 
 6.50 
 
 5.76 
 
 .52 
 
 "T78 
 
 T76 
 
 -5J2 
 
 T74 
 
 "58 
 
 PH 
 
 03 18 
 
 8.09 
 
 6.84 
 
 6.14 
 
 5.44 
 
 .58 
 
 6.41 
 
 5.44 
 
 4.83 
 
 4.48 
 
 .65 
 
 fa 19 
 
 7J86 
 
 "O8 ""f)"s2 
 
 Tl5 
 
 -64 
 
 6.07 
 
 5.15 
 
 4.57 
 
 4.24 
 
 .72 
 
 20 
 
 7.28 
 
 e!i6i s!52 
 
 4.90 
 
 .71 
 
 5.76 
 
 4.89 
 
 4.34 
 
 4.03 
 
 .80 
 
 21 
 
 6.93 
 
 5.86 5.25 
 
 4.66 
 
 .78 
 
 5.49 
 
 4.66 
 
 4.14 
 
 3.84 
 
 .88 
 
 H 22 
 
 6.62 
 
 5.60 5.02 
 
 4.45 
 
 .86 
 
 5.24 
 
 4.45 
 
 3.95 
 
 3.07 
 
 .97 
 
 23 
 
 6.33 
 
 5.8o| 4.80 
 
 4.25 
 
 .94 
 
 5.01 
 
 4.25 
 
 3.78 
 
 3.50 
 
 1.06 
 
 W 24 
 
 6.07 
 
 5.13! 4.61 
 
 4.08 
 
 1.02 
 
 4.80 
 
 4.08 
 
 3.62 
 
 3.36 
 
 1.16 
 
 K; 25 
 
 5.82 
 
 4.93 4.42 
 
 3.92 
 
 1.11 
 
 4.61 
 
 3.91 
 
 3.48 
 
 3.22 
 
 1.26 
 
 26 
 
 5.60 
 
 4.74 4.25 
 
 3.77 
 
 1.21 
 
 4.43 
 
 3.77 
 
 3.34 
 
 3.10 
 
 1.36 
 
 27 
 
 5.39 
 
 4.561 4.09 
 
 3.631.30 
 
 4.27 
 
 3.62 
 
 3.22 
 
 2.98 
 
 1.46 
 
 28 
 
 5.20 
 
 4.40 3.95 
 
 3.50 1.40 
 
 4.12 
 
 3.50 
 
 3.10 
 
 2.88 
 
 1.57 
 
 29 
 
 5.02 
 
 4.25 
 
 3.81 
 
 3.381.50 
 
 3.98 
 
 3.37 
 
 3.00 
 
 2.78 
 
 1.68 
 
TABLE OF SAFE LOADS. 
 
 7" 
 
 PENCOYD 
 
 6" 
 
 BEAMS. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for eacli size of beam. 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be ^o of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 13 
 
 13 14 
 
 14 
 
 05 
 1 
 
 15 
 
 15 
 
 16 
 
 16 
 
 5 
 
 SIZE OF BEAM 
 IN INCHES. 
 
 7" 
 
 7" 
 
 7" 
 
 7" 
 
 M 
 i- 
 
 6" 
 
 6" 
 
 6" 
 
 6" 
 
 H 
 
 WT. PER YD. 
 IN LBS. 
 
 88 
 
 75 
 
 63 
 
 51 
 
 i 
 
 to 
 
 63 
 
 55 
 
 48 
 
 40 
 
 1 
 
 (0 
 
 MOMENT OF 
 INERTIA. 
 
 58.6 
 
 53.3 
 
 48.0 
 
 43.1 
 
 O 
 
 30.8 
 
 27.5 
 
 26.3 
 
 24.1 
 
 O 
 1 
 
 
 
 
 
 
 3 
 
 
 
 
 
 3 
 
 
 
 E 
 
 
 E 
 
 
 GREATEST SAFE LOAD. 
 
 ft 
 
 GREATEST SAFE LOAD. 
 
 1 
 
 6 
 
 12.93 
 
 11.75 
 
 10.65 
 
 6.17 
 
 .08 
 
 8.03 
 
 7.42 
 
 6.87 
 
 6.25 
 
 .10 
 
 7 
 
 11.09 
 
 10.07 
 
 9.13 
 
 6.17 
 
 .11 
 
 6.89 
 
 6.36 
 
 5.89 
 
 5.36 
 
 .13 
 
 8 
 
 9.70 
 
 8.81 
 
 7.99 
 
 6.17 
 
 .15 
 
 6.02 
 
 5.56 
 
 5.15 
 
 4.C9 
 
 .17 
 
 9 
 
 8.62 
 
 7.83 
 
 7.10 
 
 6.17 
 
 .19 
 
 5.36 
 
 4.94 
 
 4.58 
 
 4.17 
 
 .22 
 
 10 
 
 7.76 
 
 7.05 
 
 6.39 
 
 5.74 
 
 .23 
 
 4.82 
 
 4.45 
 
 4.12 
 
 3.74 
 
 .27 
 
 ^ 11 
 
 7.05 
 
 6.41 
 
 5.81 
 
 5.22 
 
 .28 
 
 4.38 
 
 4.05 
 
 3.75 
 
 3.41 
 
 .32 
 
 H 12 
 
 6.47 
 
 5.87 
 
 5.32 
 
 4.79 
 
 .33 
 
 4.02 
 
 3.71 
 
 3.43 
 
 3.12 
 
 .38 
 
 g 13 
 
 5.97 
 
 5.42 
 
 4.92 
 
 4.41 
 
 .38 
 
 T77 
 
 nra 
 
 TIT 
 
 T^ 
 
 "43 
 
 fc 14 
 
 5.54 
 
 5.04 
 
 4.56 
 
 4.10 
 
 .44 
 
 3.44 
 
 3.18 
 
 2.94 
 
 2.68 
 
 .52 
 
 15 
 
 TTT 
 
 "4*70 
 
 T38 
 
 -O 
 
 "51 
 
 3.21 
 
 2.97 
 
 2.75 
 
 2.50 
 
 .60 
 
 fc 16 
 
 4.85 
 
 4.41 
 
 3.99 
 
 3.59 
 
 .58 
 
 3.01 
 
 2.78 
 
 2.57 
 
 2.34 
 
 .69 
 
 <5 17 
 
 4.5(3 
 
 4.15 
 
 3.76 
 
 3.38 
 
 .66 
 
 2.84 
 
 2.62 
 
 2.42 
 
 2.21 
 
 .78 
 
 PH 
 
 
 
 
 
 
 
 
 
 
 
 60 18 
 
 4.31 
 
 3.92 
 
 3.55 
 
 3.19 
 
 .74 
 
 2.68 
 
 2.47 
 
 2.29 
 
 2.08 
 
 .87 
 
 fc 19 
 
 4.08 
 
 3.71 
 
 3.36 
 
 3.0-2 
 
 .82 
 
 2.54 
 
 2.34 
 
 2.17 
 
 1.97 
 
 .97 
 
 20 
 
 3.88 
 
 3.52 
 
 3.19 
 
 2.87 
 
 .90 
 
 2.41 
 
 2.22 
 
 2.06 
 
 1.87 
 
 1.07 
 
 21 
 
 3.70 
 
 3.36 
 
 3.04 
 
 2.73 
 
 .99 
 
 2.30 
 
 2.12 
 
 1.96 
 
 1.78 
 
 1.18 
 
 M 
 
 
 
 
 
 
 
 
 
 
 
 EH 0-2 
 
 3.53 
 
 3.20 
 
 2.90 
 
 2.61 
 
 1.09 
 
 2.19 
 
 2.02 
 
 1.87 
 
 1.70 
 
 1.29 
 
 S 23 
 
 3.37 
 
 3.07 
 
 2.77 
 
 2.491.20 
 
 2.10 
 
 1.93 
 
 1.79 
 
 1.63 
 
 1.41 
 
 g 24 
 
 3.23 
 
 2.94 
 
 2.66 
 
 2.39 1.33 
 
 2.01 
 
 1.85 
 
 1.72 
 
 1. 5611.54 
 
 3 25 
 
 3.10 
 
 2.82 
 
 2 56 
 
 2.30 
 
 1.43 
 
 1.93 
 
 1.78 
 
 1.65 
 
 1.50 
 
 1.67 
 
 26 
 
 2.98 
 
 2.71 
 
 2.46 
 
 2.21 
 
 1.55 
 
 1.85 
 
 1.71 
 
 1.58 
 
 1.44 
 
 1.81 
 
 27 
 
 2.87 
 
 2.61 
 
 2.37 
 
 2.121.67 
 
 1.78 
 
 1.65 
 
 1.53 
 
 1.39,1.95 
 
 28 
 
 2.77 
 
 2.52 
 
 2.28 
 
 2.051.80 
 
 1.72 
 
 1.59 
 
 1.47 
 
 1.34 2.10 
 
 29 
 
 2.68 
 
 2.43 
 
 2.20 
 
 1.981.93 
 
 1.66 
 
 1.53 
 
 1.42 
 
 1.2912.25 
 
 
 
 
 
 
 
 
 
 
 
 
44 
 
 WROUGHT IRON AND STEEL. 
 
 5" 
 
 PENCOYD 
 
 BEAMS. 
 
 4" 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of beam. 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be & of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 17 
 
 17 
 
 18 
 
 18 
 
 oc 
 
 
 1 
 
 19 
 
 19 
 
 20. 
 
 20. 
 
 ai 
 
 m 
 
 SIZE OF BEAM 
 IN INCHES. 
 
 5" 
 
 5" 5" 
 
 5" 
 
 ~ 
 
 H 
 
 is 
 
 4" 
 
 4" | 4" 
 
 4" 
 
 w 
 
 
 Tj< 
 
 WT. PER YD. 
 IN LBS. 
 
 40 
 
 36 33 
 
 30 
 
 M 
 
 tt 
 
 38 28 
 
 21.5 
 
 18.5 
 
 03 
 
 ^ 
 
 MOMENT op 
 INERTIA. 
 
 14.7 
 
 13.7 
 
 13.1 
 
 12.5 
 
 LECTIO! 
 
 9.0 
 
 7.7 
 
 5.5 
 
 5.1 
 
 O 
 
 
 GREATEST SAFE LOAD. 
 
 h 
 
 a 
 P 
 
 GREATEST SAFE LOAD. 
 
 W 
 ft 
 
 4 
 
 6.80 
 
 6.42 
 
 6.12 
 
 4.86 
 
 .05 
 
 5.25 
 
 4.47 3.27 
 
 3.00 
 
 .06 
 
 5 
 
 5.44 
 
 5.14 
 
 4.90 
 
 4.67 
 
 .08 
 
 4.25 
 
 3.58 
 
 2.6-2 
 
 2.40. .10 
 
 6 
 
 4.53 
 
 4.28 
 
 4.08 
 
 3.89 
 
 .12 
 
 3.50 
 
 2.98 
 
 2.18 
 
 2.00 
 
 .14 
 
 7 
 
 3.89 
 
 3 67 
 
 3.50 
 
 3.33 
 
 .16 
 
 3.00 
 
 2.56 
 
 1.86 
 
 1.71 
 
 .20 
 
 8 
 
 3.40 
 
 3.21 
 
 3.06 
 
 2.92 
 
 .21 
 
 2.62 
 
 2.24 
 
 1.64 
 
 1.50 
 
 .28 
 
 FH 9 
 
 3.02 
 
 2.86 
 
 2.72 
 
 2.59 
 
 .26 
 
 ~33 
 
 i.yy 1.46 
 
 TB 
 
 -33 
 
 H 10 
 
 2.72 
 
 2.57 
 
 2.45 
 
 2.33 
 
 .32 
 
 2.10 
 
 1.79 
 
 1.31 
 
 1.20 
 
 .40 
 
 11 
 
 7 
 
 TM 
 
 "T23 
 
 "TT2 
 
 "39 
 
 1.91 
 
 1.63 
 
 1.19 
 
 1.09 
 
 .49 
 
 K 12 
 
 2.27 
 
 2.14 
 
 2.04 
 
 1.94 
 
 .46 
 
 1.75 
 
 1.49 
 
 1.09 
 
 1.00 
 
 .58 
 
 M 13 
 
 2.09 
 
 .98 
 
 .88 
 
 1.79 
 
 .54 
 
 1.62 
 
 1.88 
 
 1.01 
 
 .92 
 
 .68 
 
 fc H 
 
 1.94 
 
 .84 
 
 .75 
 
 1.67 
 
 .63 
 
 1.50 
 
 1.28 
 
 .94 
 
 86 
 
 .79 
 
 3 15 
 
 1.81 
 
 .71 
 
 .63 
 
 1.55 
 
 .72 
 
 1.40 
 
 1.19 
 
 .87 
 
 80 
 
 .91 
 
 OH 
 
 
 
 
 
 
 
 
 
 
 
 50 16 
 
 .70 
 
 .61 
 
 .53 
 
 1.46 
 
 .82 
 
 1.31 
 
 1.12 
 
 .82 
 
 .75 
 
 1.03 
 
 EC, 17 
 
 .60 
 
 .51 
 
 .44 
 
 1.37 
 
 .93 
 
 1.23 
 
 1.05 
 
 .77 
 
 .71 1.17 
 
 18 
 
 .51 
 
 .43 
 
 .36 
 
 1.30 
 
 1.04 
 
 1.17 
 
 .1)9 
 
 .73 
 
 .671.31 
 
 19 
 
 .43 
 
 .35 
 
 .29 
 
 1.23 
 
 1.16 
 
 1.11 
 
 .94 
 
 .69 
 
 .631.48 
 
 PS 
 
 
 
 
 
 
 
 
 
 
 
 20 
 
 .36 
 
 .28 
 
 .22 
 
 1.17 
 
 1.29 
 
 1.05 
 
 .89 
 
 .65 
 
 .60 
 
 1.61 
 
 25 21 
 
 .29 
 
 .22 
 
 .17 
 
 1.11 1.42 
 
 1.00 
 
 .85 
 
 ,6'2 
 
 .571.77 
 
 23 
 
 .24 
 
 .17 
 
 .11 
 
 l.Olil.58 
 
 .95 
 
 .81 
 
 .60 
 
 .541.93 
 
 3 23 
 
 .18 
 
 .12 
 
 .07 
 
 1.01 
 
 1.70 
 
 .91 
 
 .78 
 
 .57 
 
 .522.12 
 
 24 
 
 .13 
 
 1.07 
 
 1.02 
 
 .97 
 
 1.85 
 
 .87 
 
 .75 
 
 .55 
 
 .50,2.32 
 
 25 
 
 .09 
 
 1.03 
 
 .98 
 
 .93 2.01 
 
 .84 
 
 .7-2 
 
 .52 
 
 .48^2.51 
 
 26 
 
 .04 
 
 .99 
 
 .94 
 
 .902.18! 
 
 .81 
 
 .69 
 
 .50 
 
 .46 2.71 
 
 27 
 
 1.01 
 
 .95 
 
 .91 
 
 .86 
 
 2.36 
 
 .78 
 
 .66 
 
 .48 
 
 .44 
 
 2.91 
 
TABLE OF SAFE LOADS. 
 
 45 
 
 PENCOYD 
 
 BEAMS. 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed including beam itself. 
 Deflections in inches corresponding to given loads for each size of beam. 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be 'nT of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 21 
 
 21 
 
 22 
 
 22 
 
 a 
 
 
 
 
 
 SIZE OP BEAM 
 IN INCHES. 
 
 3" 
 
 3" 
 
 3" 
 
 3" 
 
 | 
 
 
 
 
 
 WT. PER YD. 
 IN LBS. 
 
 28.6 
 
 23 
 
 21.7 
 
 17 
 
 2 
 
 OB 
 
 
 
 
 
 MOMENT op 
 INERTIA. 
 
 4.0 
 
 3.3 
 
 3.0 
 
 2.7 
 
 I 
 
 
 
 
 
 
 GREATEST SAFE LOAD. 
 
 1 
 
 
 4 
 
 2.87 
 
 2.56 
 
 2.34 
 
 2.07 
 
 .09 
 
 
 
 
 
 5 
 
 2.30 
 
 2.05 
 
 1.87 
 
 1.88 
 
 .14 
 
 
 
 
 
 6 
 
 1.92 
 
 1.71 
 
 1.56 
 
 1.38 
 
 .19 
 
 
 
 
 
 7 
 
 -1-64 
 
 HT1& 
 
 "T34 
 
 -n 
 
 "26 
 
 
 
 
 
 &3 8 
 
 1.44 
 
 1.28 
 
 1.17 
 
 1.03 
 
 .34 
 
 
 
 
 
 fe 9 
 
 1.28 
 
 1.14 
 
 1.04 
 
 .92 
 
 .43 
 
 
 
 
 
 ^ 10 
 
 1.15 
 
 1.02 
 
 .94 
 
 .82 
 
 .53 
 
 
 
 
 
 S 11 
 
 1.04 
 
 .93 
 
 .85 
 
 .75 
 
 .65 
 
 
 
 
 
 fc 12 
 
 .96 
 
 .85 
 
 .78 
 
 .69 
 
 .77 
 
 
 
 
 
 ^ 13 
 3 14 
 15 
 
 .88 
 .82 
 .77 
 
 .79 
 .73 
 
 .68 
 
 .72 
 .67 
 .62 
 
 .64 
 .59 
 .55 
 
 .91 
 
 1.05 
 1.21 
 
 
 
 
 
 C 16 
 
 17 
 g 18 
 
 | 
 
 .64 
 .60 
 .57 
 
 .58 
 .55 
 .52 
 
 .521.37 
 .491.55 
 .4611.74 
 
 
 
 
 
 g 19 
 
 .61 
 
 .54 
 
 .49 
 
 .44 
 
 1.93 
 
 
 
 
 
 W 20 
 
 .58 
 
 .51 
 
 .47 
 
 .41 
 
 2.13 
 
 
 
 
 
 ^ 21 
 
 .55 
 
 .49 
 
 .45 
 
 .39 
 
 2.37 
 
 
 
 
 
 22 
 
 .52 
 
 .47 
 
 .43 
 
 .38 
 
 2.62 
 
 
 
 
 
 23 
 
 .50 
 
 .44 
 
 .41 
 
 .36 
 
 2.88 
 
 
 
 
 
46 
 
 WROUGHT IKON AND STEEL. 
 
 PENCOYD 
 
 15" 
 
 CHANNELS. 
 
 12" 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of channel. 
 For a load in middle of beam, allow one-half the tabular figures. 
 Deflection for latter load will be -fa of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 30 
 
 30 
 
 
 
 $ 
 
 w 
 
 31 
 
 31 
 
 32 
 
 32 
 
 w 
 
 SIZE OF CHAN- 
 NEL IN INS. 
 
 15" 
 
 15" 
 
 
 
 fc 
 BE 
 
 12" 
 
 12" 
 
 12" 
 
 12" 
 
 3 
 
 WT. PER YD. 
 IN LBS. 
 
 204.5 
 
 148 
 
 
 
 K 
 
 160 
 
 88.5 
 
 101.5 
 
 60 
 
 1 
 
 8 
 
 
 
 
 
 
 
 
 
 
 
 g 
 
 
 
 
 
 
 
 
 
 
 MOMENT OF 
 INERTIA. 
 
 557.4 
 
 451.5 
 
 
 
 CO 
 
 'EH 
 
 g 
 
 268.5 
 
 182.7 
 
 173.5 
 
 123.7 
 
 03 
 
 
 GREATEST SAFE LOAD. 
 
 1 
 
 GREATEST SAFE LOAD. 
 
 d 
 1 
 
 10 
 
 34.68 
 
 28.09 
 
 
 
 .11 
 
 20.88 
 
 14.21 
 
 13. 4C 
 
 9.14 
 
 .13 
 
 11 
 
 31.53 
 
 25.54 
 
 
 
 .13 
 
 18.98 
 
 12.!I2! 12.26 
 
 8.75 
 
 .16 
 
 12 
 
 28.90 
 
 23.41 
 
 
 
 .15 
 
 17.40 
 
 11.84 : 11.24 
 
 8.02 
 
 .19 
 
 13 
 
 26. 63 
 
 21.61 
 
 
 
 .18 
 
 16.06 
 
 10.93 10.38 
 
 7.40 
 
 .22 
 
 14 
 
 24.77 
 
 20.08 
 
 
 
 .21 
 
 14.91 
 
 10.15 9.64 
 
 6.87 
 
 .26 
 
 EH 15 
 
 23.12 
 
 18.73 
 
 
 
 .24 
 
 13.1(2 
 
 9.47i 8.99 
 
 6.41 
 
 .30 
 
 W 16 
 
 21.68 
 
 17.56 
 
 
 
 .27 
 
 13.05 
 
 8.88 
 
 8.43 
 
 6.01 
 
 .34 
 
 g 17 
 
 20.40 
 
 16.52 
 
 
 
 .30 
 
 12.28 
 
 8.36 
 
 7.94 
 
 5.66 
 
 .38 
 
 !z 18 
 
 19.27 
 
 15.61 
 
 
 
 .34 
 
 11.60 
 
 7.89 
 
 ' 7.49 
 
 5.34 
 
 .43 
 
 B 19 
 
 18.25 
 
 It. 78 
 
 
 
 .38 
 
 10.99 
 
 7.48 
 
 7.10 
 
 5.06 
 
 .48 
 
 20 
 
 17.34 
 
 14.04 
 
 
 
 .43 
 
 10.44 
 
 7.10 
 
 6.74 
 
 4.81 
 
 .53 
 
 5 21 
 
 16.52 
 
 13.38 
 
 
 
 .47 
 
 9.94 
 
 6.77 
 
 6.42 
 
 4.58 
 
 .58 
 
 OQ 22 
 
 15.76 
 
 12.77 
 
 
 
 .52 
 
 9.49 
 
 6.46 
 
 6.13 
 
 4.37J .64 
 
 23 
 
 15.08 
 
 12.21 
 
 
 
 .57 
 
 9.08 
 
 6.18 
 
 5.87 
 
 4.18i .70 
 
 PM 24 
 
 14.45 
 
 11.70 
 
 
 
 .62 
 
 8.70 
 
 5.92 
 
 5.62 
 
 4.01 .77 
 
 25 
 
 13.87 
 
 11.24 
 
 
 
 .67 
 
 8.35 
 
 _5.(i8 
 
 5.40 
 
 3.85 
 
 .83 
 
 g 36 
 
 13.34 
 
 10.80 
 
 
 
 .73 
 
 8M 
 
 5.47 
 
 5.19 
 
 3.70 
 
 .90 
 
 O 27 
 
 12.85 
 
 10.40 
 
 
 
 78 
 
 7.73 
 
 5.26 
 
 5.00 
 
 3.56 
 
 .97 
 
 28 
 
 12.39 
 
 10.03 
 
 
 
 84 
 
 7.46 
 
 5.07 
 
 4.82 
 
 3.44 1 05 
 
 3 29 
 
 11.96 
 
 9.69 
 
 
 
 .90 
 
 7.20 
 
 4.90 
 
 4.65 
 
 3!32lll2 
 
 30 
 
 11.56 
 
 9.36 
 
 
 
 .96 
 
 6.96 
 
 4.74 
 
 4.50 
 
 3.21,1.20 
 
 31 
 
 11.19 
 
 9.06 
 
 
 
 1.03 
 
 6.74 
 
 4.58 
 
 4.35 
 
 3.101.28 
 
 32 
 
 TOl 
 
 "T78 
 
 ^^^ 
 
 ^"^ 
 
 iTo 
 
 6.52 
 
 4.44 
 
 4.22 
 
 3.0111.36 
 
 33 
 
 10.51 
 
 8.51 
 
 
 
 1.17 
 
 6.33 
 
 4.31 
 
 4.09 
 
 2.921.44 
 
TABLE OF SAFE LOADS. 
 
 47 
 
 PENCOYD 
 
 10" 
 
 CHANNELS. 
 
 9" 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of channel. 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be -j 8 - of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 34 
 
 34 
 
 35 
 
 35 
 
 H 
 
 & 
 
 36 
 
 36 
 
 37 
 
 37 
 
 i 
 
 SlZEOFCHAN- 
 NEL IN INS. 
 
 10" 
 
 10" 
 
 10" 
 
 10" 
 
 <! 
 
 9" 
 
 9" 
 
 9" 
 
 9" 
 
 CHANN 
 
 WT. PER YD. 
 IN LBS. 
 
 106 
 
 60 
 
 86.5 
 
 49 
 
 O 
 B9 
 
 93 
 
 54 
 
 61 
 
 37 
 
 * 
 
 
 
 
 
 
 P 
 
 
 
 
 
 p 
 
 MOMENT op 
 INERTIA. 
 
 131.0 
 
 92.7 
 
 105.2 
 
 73.9 
 
 HH 
 
 90.7 
 
 64.3 
 
 59.8 
 
 43.6 
 
 fe 
 
 jn 
 
 
 GREATEST SAFE LOAD. 
 
 M 
 
 GREATEST SAFE LOAD. 
 
 I 
 
 10 
 
 12.23 
 
 8.65 
 
 9.81 
 
 6.89 
 
 .16 
 
 9.41 
 
 6.67 
 
 6.21 4.52 
 
 .18 
 
 11 
 
 11.12 
 
 7.86 
 
 8.92 
 
 6.26 
 
 .19 
 
 8.55 
 
 6. re 
 
 5.65 4.11 
 
 .22 
 
 12 
 
 10.19 
 
 7 21 
 
 8.17 
 
 5.74 
 
 .23 
 
 7.84 
 
 5.56 
 
 5.17 3.77 
 
 .28 
 
 13 
 
 9.41 
 
 6^65 
 
 7.55 
 
 5.30 
 
 .27 
 
 7.24 
 
 5.13 
 
 4.78 
 
 3.48 
 
 .30 
 
 14 
 
 8.74 
 
 6.18 
 
 7.01 
 
 4.92 
 
 .31 
 
 6.72 
 
 4.76 
 
 4.44 
 
 3.23 
 
 .35 
 
 E-i 15 
 
 8.15 
 
 5.77 
 
 6.54 
 
 4.59 
 
 .36 
 
 6.27 
 
 4.45 
 
 4.14 3.01 
 
 .40 
 
 g 16 
 
 7.64 
 
 5.41 
 
 6.13 
 
 4.31 
 
 .41 
 
 5.88 
 
 4.17 
 
 3.88 2.82 
 
 .46 
 
 
 7.19 
 
 5.09 
 
 5.77 
 
 4.05 
 
 .46 
 
 5.53 
 
 3.92 
 
 3.65, 2.66 
 
 .52 
 
 & 18 
 
 6.79 
 
 4.81 
 
 5.45 
 
 3.83 
 
 .52 
 
 5.23 
 
 3.71 
 
 3.45 2.51 
 
 .58 
 
 19 
 
 20 
 
 6.44 
 
 6.11 
 
 4.55 
 4.32 
 
 5.16 
 4.90 
 
 3.63 
 
 3.44! 
 
 .58 
 .641 
 
 T95 
 4.70 
 
 "TsT 
 
 3.34 
 
 3.27 TT38 
 3.10 2.26 
 
 TB 
 
 .71 
 
 
 5.82 
 
 Tl2 
 
 Te? 
 
 fa 
 
 4.48 
 
 3.18 
 
 2.96 2.15 
 
 .78 
 
 00 22 
 
 5.56 
 
 3.93 
 
 4.46 
 
 3.131 .78 
 
 4.28 3.03 
 
 2.S2 
 
 2.05 
 
 .86 
 
 fe 23 
 
 5.32 
 
 3.76 
 
 4.27 
 
 2.99 
 
 .85 
 
 4.09 2.90 
 
 2.70 
 
 1.97 
 
 
 24 
 
 5.10 
 
 3.60 
 
 4.09 
 
 2.87 
 
 .92 
 
 3.92 2.78 
 
 2.59 
 
 1.88 
 
 l!02 
 
 M 25 
 
 4.89 
 
 3.46 
 
 3.92 
 
 2.761.00 
 
 3.76 2.67 
 
 2.48 
 
 1.81 
 
 1.11 
 
 g o 6 
 
 rh 26 
 
 4.70 
 
 3.33 
 
 3.77 
 
 2.65 
 
 1.C8 
 
 3.62 
 
 2.57 
 
 2.39 
 
 1.74 
 
 1.21 
 
 fc 27 
 
 4.53 
 
 3.20 
 
 3.63 
 
 2.55 1.17 
 
 3.49 
 
 2.47 
 
 2.30 
 
 1.67 
 
 1.30 
 
 W 28 
 
 4.37 
 
 3.09 
 
 3.50 
 
 2.461.26 
 
 3.36 
 
 2.38 
 
 2.22 
 
 1.61 
 
 1.40 
 
 ^ 29 
 
 4.22 
 
 2.98 
 
 3.38 
 
 2.38 1.35 
 
 3.24 
 
 2.30 
 
 2.14 
 
 1.56 
 
 .50 
 
 30 
 
 4.08 
 
 2.88 
 
 3.27 
 
 2.301.45 
 
 3.14 
 
 2.22 
 
 2.07 
 
 1.51 
 
 .61 
 
 31 
 
 3.94 
 
 2.79 
 
 3.16 
 
 2.221.55 
 
 3.03! 2.15 
 
 2.00 1.46 
 
 1.72 
 
 32 
 
 3.82 
 
 2.70 
 
 3.07 
 
 2.151.65 
 
 2.94 
 
 2.08 
 
 1.94! 1.41 
 
 1.83 
 
 33 
 
 3.71 
 
 2.62 
 
 2.97 
 
 2.09 
 
 1.76 
 
 2.85 
 
 2.02 
 
 1.88 
 
 1.37 
 
 1.95 
 
48 
 
 PENCOYD 
 
 WROUGHT IRON AND STEEL, 
 
 8" 
 
 CHANNELS. 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflection in inches corresponding to given loads for each size of channel. 
 For load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be -ur of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 38 
 
 38 
 
 39 
 
 39 
 
 ? 
 
 40 
 
 40 
 
 41 
 
 41 
 
 * 
 
 SlZEOFCHAN- 
 NEL IN INS. 
 
 
 
 
 
 a 
 o 
 
 7" 
 
 7" 
 
 7" 
 
 7" 
 
 I 
 
 8'' 
 
 8" 
 
 8" 
 
 8" 
 
 WT. PER YD. 
 IN LBS. 
 
 80.5 
 
 43 
 
 54 
 
 30 
 
 00 
 
 (6 
 
 73 
 
 41 
 
 49 
 
 26 
 
 \ 
 
 MOMENT OF 
 INERTIA. 
 
 60.0 
 
 40.0 
 
 41.0 
 
 28.2 
 
 to 
 
 O 
 
 h 
 
 42.6 
 
 29.5 
 
 27.9 
 
 18.5 
 
 00 
 
 
 GREATEST SAFE LOAD. 
 
 1 
 
 GREATEST SAFE LOAD. 
 
 \ 
 
 
 
 <3 
 
 
 n 
 
 
 1 
 
 
 
 
 
 
 
 
 6 
 
 11.67 
 
 7.77 
 
 7.93 
 
 4.79 .07 
 
 9.45 6.55 
 
 6.18 
 
 3.42 
 
 .08 
 
 7 
 
 10.00 
 
 6.66 
 
 6.83 
 
 4.70 .10 
 
 8.10 5.61 
 
 5.30 
 
 3.42 
 
 .11 
 
 8 
 
 8.75 
 
 5.83 
 
 5.97 
 
 4.11 .13 
 
 7.09 4.91 
 
 4.64 
 
 3.07 
 
 .15 
 
 9 
 
 7.78 
 
 5.18 
 
 5.31 
 
 3.6 .16 
 
 6.30 4.37 
 
 4.12 
 
 2.73 
 
 .19 
 
 10 
 
 7.00 
 
 4.66 
 
 4.78 
 
 3.29 .20 
 
 5.67, 3.93 
 
 3.71 
 
 2.46 
 
 .23 
 
 gll 
 
 6.36 
 
 4.24 
 
 4.35 
 
 2.99 .24 
 
 5.15 3.57 
 
 3.37 
 
 2.24 
 
 .28 
 
 1-2 
 
 5.83 
 
 3.88 
 
 3.98 
 
 2.74 .29 
 
 4.72 3.27 
 
 3.09 
 
 2.05 
 
 ,33 
 
 g I 3 
 
 5.38 
 
 3. 58 
 
 3.67 
 
 2.53 
 
 .34 
 
 4.36 3.02 
 
 2.85 
 
 1.89 
 
 .38 
 
 14 
 
 5.00 
 
 3.33 
 
 3.41 
 
 2.35 
 
 .39 
 
 4.05 2.81 
 
 2.65 
 
 1.76 
 
 .45 
 
 "-' 15 
 
 4.67 
 
 3.11 
 
 3.19 
 
 2.19 
 
 .45 
 
 ~3"78"T62 
 
 "T47 
 
 T64 
 
 T2 
 
 >-T 16 
 
 4.37 
 
 2.91 
 
 2.99 
 
 2.06 
 
 .51 
 
 3.54 2.46 
 
 2.32 
 
 1.54 
 
 .59 
 
 < 17 
 
 -os 
 
 "Tr4 
 
 T8I 
 
 HT4 
 
 -58 
 
 3.34 2.31 
 
 2.18 
 
 1.45 
 
 .67 
 
 * 18 
 
 3.89 
 
 2.59 
 
 2.66 
 
 1.83 
 
 .65 
 
 3.15 
 
 2.18 
 
 2.06 
 
 .37 
 
 .75 
 
 fr 19 
 
 3.68 
 
 2.45 
 
 2.52 
 
 1.73 
 
 .72 
 
 2.98 2.07 
 
 1.95 
 
 .29 
 
 .83 
 
 20 
 
 3.50 
 
 2.33 
 
 2.39 
 
 1.64 
 
 .80 
 
 2.83 1.96 
 
 1.85 
 
 .23 
 
 .92 
 
 21 
 
 3.33 
 
 2.22 
 
 2. 8 
 
 1.57 
 
 .88 
 
 2.70 1.87 
 
 1.77 
 
 .17 
 
 1.01 
 
 E-| 2 
 
 3.18 
 
 2.12 
 
 2.17 
 
 1.50 
 
 .97 
 
 2.58 1.79 
 
 1.69 
 
 .121.11 
 
 i 2:i 
 
 3.04 
 
 2.03 
 
 2.08 
 
 1.43 
 
 1.06 
 
 2.47 1.71 
 
 1.61 
 
 .071.22 
 
 W 24 
 
 2.92 
 
 1.94 
 
 1.99 
 
 1.37 
 
 1.16 
 
 2.36 1.64 
 
 1.55 
 
 .021.34 
 
 H; 25 
 
 2.80 
 
 1.86 
 
 1.91 
 
 1.32 
 
 1.26 
 
 2.27J 1.57 
 
 1.48 
 
 .98jl.45 
 
 26 
 
 2 61 
 
 1.79 
 
 1.84 
 
 1.26 
 
 1.36 
 
 2.18 
 
 1.51 
 
 1.43 
 
 .95'l.57 
 
 27 
 
 2.59 
 
 1.73 
 
 1.77 1.22 
 
 1.46 
 
 2.10 1.46 
 
 1.37 
 
 .91J1.69 
 
 28 
 
 2.50 
 
 1.66 
 
 1.71 1.17 
 
 1.57 
 
 2.02 1.40 
 
 1.32 
 
 .88 1.82 
 
 89 
 
 2.41 
 
 1.61 
 
 1.65 
 
 1.13 
 
 1.68 
 
 1.95 
 
 1.35 
 
 1.28 
 
 .851.95 
 
TABLE OF SAFE LOADS. 
 
 PENCOYD 
 
 H 5" and 6" jl 
 
 3" and 4" 
 
 CHANNELS. 
 
 Maximum and Minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed including beam itself. 
 Deflections in inches corresponding to given loads for each size of chanm* 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be TJ of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 3 
 
 42 
 
 44 
 
 45 
 
 46 
 
 M 
 
 g 
 
 47 
 
 48 
 
 49 
 
 49 
 
 1 
 
 
 W 
 
 
 
 
 
 
 
 
 
 
 
 
 SIZE OF ! 
 
 \ 
 
 
 
 
 
 * 
 
 
 
 
 
 
 * 
 
 CHANNEL 
 IN INS. 
 
 I 
 
 6" 
 
 6" 
 
 5" 
 
 5" 
 
 3 
 
 5 
 
 
 
 
 
 5 
 
 ~WT. PER 
 
 
 
 
 
 
 ^ 
 
 * 
 
 
 
 
 
 cb 
 
 YD. IN 
 
 b 
 
 33.0 
 
 23 
 
 27 
 
 18.8 
 
 o 
 
 r* 
 
 21.5 
 
 17.5 
 
 18.9 
 
 15.2 
 
 g 
 
 LBS. 
 
 o 
 
 
 
 
 
 
 
 
 
 PH 
 
 
 
 
 
 
 fr 
 
 MOM. OF 
 INERTIA. 
 
 1 
 
 18.4 
 
 11.7 
 
 10.3 
 
 6.7 
 
 fe 
 
 fc 
 
 5.2 
 
 4.1 
 
 2.3 
 
 2.0 
 
 1 
 
 
 3 
 
 1 
 
 GREATEST SAFE LOAD. 
 
 K 
 
 K 
 ft 
 
 ft 
 
 GREATEST SAFE LOAD. 
 
 ft 
 
 
 .02 
 
 6.50 
 
 5.24 
 
 5.92 
 
 4.13 
 
 .02 
 
 .03 
 
 4.03 3.20 
 
 2.40 
 
 2.10 
 
 .05 
 
 4 
 
 .04 
 
 6.50 
 
 4.54 
 
 4.80 
 
 3.10 
 
 .05 
 
 .06 
 
 3.02, 2.40 
 
 1.80 
 
 1.57 
 
 .09 
 
 5 
 
 .07 
 
 5.70 
 
 3.63 
 
 3.84 
 
 2.48 
 
 .08 
 
 .10 
 
 2.42 1.92 
 
 1.44 
 
 1.26 
 
 .14 
 
 FH' 6 
 
 .10 
 
 4.75 
 
 3.02 
 
 3.20 
 
 2.07 
 
 .12 
 
 .14 
 
 2.02 
 
 1.60 
 
 1.20 
 
 1.05 
 
 /L9 
 
 &3 7 
 
 .13 
 
 4.07 
 
 2.59 
 
 2.74 
 
 1.77 
 
 .16 
 
 .20 
 
 1.73 
 
 1.37 
 
 1.03 
 
 .90 
 
 .26 
 
 ^ 8 
 
 .17 
 
 3.56 
 
 2.26 
 
 2.40 
 
 1.55 
 
 .21 
 
 .2* 
 
 1.51 1 1.20 
 
 .90 
 
 .79 
 
 .34 
 
 Y-r 9 
 
 .22 
 
 3.17 
 
 2.01 
 
 2.13 
 
 1.38 
 
 .26 
 
 
 
 O)7 
 
 .80 
 
 .70 
 
 .43 
 
 K 10 
 
 .27 
 
 2.85 
 
 1.81 
 
 1.92 
 
 1.24 
 
 .32 
 
 .40 
 
 1.21 
 
 .96 
 
 .72 
 
 .63 
 
 .53 
 
 % n 
 
 .32 
 
 2.59 
 
 1.64 
 
 1.74 
 
 1.13 
 
 .39 
 
 .49 
 
 1.10 
 
 .87 
 
 .65 
 
 .57 
 
 .65 
 
 PH 12 
 
 .38 
 
 2.37 
 
 1.51 
 
 1.60 
 
 1.03 
 
 .46 
 
 .58 
 
 1.01 
 
 .80 
 
 .60 
 
 .52 
 
 .77 
 
 W 13 
 
 "45 
 
 2.19 
 
 ""7^J9 
 
 1.48 
 
 .95 
 
 .54 
 
 .68 
 
 .93 
 
 .74 
 
 .?5 
 
 .48 
 
 .91 
 
 fe 14 
 
 .52 
 
 2.04 
 
 i!s3 
 
 1.37 
 
 .89 
 
 .63 
 
 .79 
 
 .86 
 
 .69 
 
 !51 
 
 .45 
 
 1.05 
 
 C 
 
 
 
 
 
 
 
 
 
 
 
 
 15 
 
 .60 
 
 1 90 
 
 1.21 1.28 
 
 .83! .72 
 
 .91 
 
 .81 
 
 .64 
 
 .48 
 
 .42 
 
 1.21 
 
 5 16 
 
 .69 
 
 1.78 
 
 1.13 1.20 
 
 .77 .82 
 
 1.03 
 
 .76 
 
 .60 
 
 .45 
 
 .39 
 
 1.37 
 
 g 17 
 
 .78 
 
 1.H8 
 
 1.06 1.13 
 
 .73 .93 
 
 1.17 
 
 .71 
 
 .56 
 
 .42 
 
 .37 
 
 1.55 
 
 | 18 
 
 .87 
 
 1.58 
 
 1.01 
 
 1.07 
 
 .691.04 
 
 1.31 
 
 .67 
 
 .53 
 
 .40 
 
 .35 
 
 1.74 
 
 ^ 19 
 
 .97 
 
 1.50 
 
 .95 
 
 1.01 
 
 .651.16 
 
 1.46 
 
 .64 
 
 .n 
 
 .38 
 
 .33 
 
 1.93 
 
 20 
 
 1.07 
 
 1.42 
 
 .90 .96 
 
 .621.29 
 
 1.61 
 
 .60 
 
 .48 
 
 .36 
 
 .31 
 
 2.13 
 
 21 
 
 1.18 
 
 1.36 
 
 .86! .91 
 
 .591.421 1.77 
 
 .58 
 
 .46! .34 
 
 .SO 
 
 2.37 
 
 22 
 
 1.29; 1.30 
 
 .82 .87 
 
 .56 1.56 
 
 1.93 
 
 .55 
 
 .44 
 
 .33 
 
 .29 
 
 2.62 
 
 23 
 
 1.41 
 
 1.24 
 
 .79 .83 
 
 .541.70 
 
 2.12 
 
 .53 
 
 .42 
 
 .31 
 
 .27 
 
 2.88 
 
 24 
 
 1.54 
 
 1.19 
 
 .75 .80 
 
 .52 1.85 12.32 
 
 50 
 
 .40 
 
 .30 
 
 26 
 
 3.11 
 
 25 
 
 1.67 
 
 1.14 
 
 .72 .77 
 
 .502.01 2.51 
 
 .48 
 
 .38 
 
 .29 
 
 .25 
 
 3.34 
 
 26 
 
 1.81 
 
 1.101 .70 .74 
 
 .482.18 
 
 1 
 
 2.71 
 
 .47 
 
 .37 
 
 .28 
 
 ,24 
 
 3.50 
 
WKOUGHT IRON AND STEEL. 
 
 PENOOYD 
 
 12" and 11" 
 
 BEAMS. 
 
 10" and 9" 
 
 Maximum and minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of beam. 
 For a load-in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be W of the tabular deflection. 
 
 CHAUT 
 
 NUMBER. 
 
 * 
 
 60 
 
 60 61 
 
 61 
 
 fi 
 
 1 
 
 oo 
 
 62 
 
 62 
 
 63 
 
 63 
 
 m 
 
 g 
 
 SIZE OF 
 
 H 
 
 
 
 
 
 M 
 
 PQ 
 
 
 
 
 
 PQ 
 
 BEAM IN 
 
 PQ 
 
 12" 
 
 12" 
 
 11" 
 
 11" 
 
 
 
 10" 
 
 10" 
 
 9" 
 
 9" 
 
 s 
 
 INCHES. 
 
 fe 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 os 
 
 WT. PER 
 
 'K 
 
 
 
 
 
 a 
 
 a 
 
 
 
 
 M 
 
 YD. IN 
 
 o 
 
 138 
 
 104 
 
 118 
 
 91 
 
 I 
 
 I 
 
 105 
 
 80 
 
 94 
 
 72 
 
 fe 
 
 LBS. 
 
 OQ 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 MOM OF. 
 INERTIA. 
 
 O 
 
 264.9 
 
 222.0 
 
 193.1 
 
 164.1 
 
 o 
 
 H 
 
 140.4 
 
 118.2 99.5 
 
 84.8 
 
 g 
 
 
 w 
 
 
 
 
 w 
 
 W 
 
 
 1 
 
 
 w 
 
 
 K 
 
 
 i 
 
 i 
 
 
 h 
 
 
 s 
 
 GREATEST SAFE LOAD. 
 
 H 
 ft 
 
 H 
 ft 
 
 GREATEST SAFE LOAD. 
 
 ft 
 
 10 
 
 .13 
 
 20.59 
 
 17.26 
 
 16.41 
 
 13.95 
 
 .15 
 
 .16 
 
 13.11 
 
 11.03 10 32 
 
 8.79 
 
 .18 
 
 11 
 
 .16 
 
 18.72 
 
 15.69 
 
 14.92 
 
 12.68 
 
 .18 
 
 .19 
 
 11.92 
 
 10.031 9.38 
 
 7.99 
 
 .22 
 
 12 
 
 .19 
 
 17.16 
 
 14.38 
 
 13.67 
 
 11.62 
 
 .21 
 
 .23 
 
 10.92 
 
 9.19 
 
 8.60 
 
 7,32 
 
 .26 
 
 13 
 
 .22 
 
 1J.84 
 
 13.28 
 
 12.62 
 
 10.73 
 
 .25 
 
 .27 
 
 10.08 
 
 8.48 
 
 7.94 
 
 6.76 
 
 .30 
 
 14 
 
 .26 
 
 14.71 
 
 12.33 
 
 11.72 
 
 9.96 
 
 .29 
 
 .31 
 
 9.36 
 
 7.88 
 
 7.37 
 
 6.28 
 
 .35 
 
 . 15 
 
 .30 
 
 13.73 
 
 11.51 
 
 10.94 
 
 9.30 
 
 
 .36 
 
 8.74 
 
 7.35 
 
 6.88 
 
 5.86 
 
 .40 
 
 B 17 
 
 34 
 
 12.87 
 
 10.79 
 
 10.26 
 
 8.72 
 
 ^39 
 
 .41 
 
 8.19 
 
 6.89 
 
 6.45 
 
 5.49 
 
 .47 
 
 
 .38 
 
 12.11 
 
 10.15 
 
 9.65 
 
 8.21 
 
 .44 
 
 .46 
 
 7.71 
 
 6.49 
 
 6.07 
 
 5.17 
 
 .53 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 18 
 
 .44 
 
 11.44 
 
 9.59 
 
 9.12 
 
 7.75 
 
 .49 
 
 .52 
 
 7.28 
 
 6.13 
 
 5.73 
 
 4.88 
 
 .59 
 
 5 19 
 
 49 
 
 10.84 
 
 9.08 
 
 8.64 
 
 7.34 
 
 .54 
 
 .58 6.90 
 
 5.81 
 
 
 4.6.3 
 
 "65 
 
 20 
 
 !54 
 
 10.29 
 
 8.63 
 
 8.20 
 
 6.97 
 
 .59 
 
 .64 
 
 6.55 
 
 5.51 
 
 5!l6 
 
 4.39 
 
 .72 
 
 * 21 
 
 .59 
 
 9.80 
 
 8.22 
 
 7.81 
 
 6.64 
 
 .65 
 
 
 6.24 
 
 -ns 
 
 4.91 
 
 4.19 
 
 .79 
 
 2 22 
 
 .65 
 
 9.36 
 
 7.8r> 
 
 7.46 
 
 6.34 
 
 .71 
 
 .78 
 
 5. 90 
 
 5.01 
 
 4.69 
 
 4.00 
 
 .87 
 
 & s 
 
 .71 
 
 8.95 
 
 7.50 
 
 -7-15 
 
 
 "77 
 
 .86 
 
 5.70 
 
 4.80 
 
 4.49 
 
 3.82 
 
 .95 
 
 o ** 
 
 .78 
 
 8.58 
 
 7.19 
 
 6.84 
 
 s!si 
 
 .84 
 
 .93 
 
 5.46 
 
 4.60 
 
 4.30 
 
 3.661.04 
 
 25 
 
 w 
 
 "84 
 
 "is 
 
 6.90 
 
 6.56 
 
 5.58 
 
 .91 
 
 1.01 
 
 5.24 
 
 4.41 
 
 4.13 
 
 3.52 
 
 1.13 
 
 
 .92 
 
 7.92 
 
 6.64 
 
 6.31 
 
 5.37 
 
 .99 
 
 1.09 
 
 5.04 
 
 4.24 
 
 3.97 
 
 3.38 
 
 1.23 
 
 ^ 27 
 
 .99 
 
 7.63 
 
 6.39 
 
 6.08 
 
 5.17 
 
 1 07 
 
 1.18 
 
 4.86 
 
 4.09 
 
 3.82 
 
 3.261.32 
 
 
 
 1.07 
 
 7.35 
 
 6.16 
 
 5.88 
 
 4.98 
 
 1.15 
 
 1.27 
 
 4.68 
 
 3.94 
 
 3.69 
 
 3.141.42 
 
 i-J 29 
 
 1.14 
 
 7.10 
 
 5.95 
 
 5.66 
 
 4.81 
 
 1.23 
 
 1.38 
 
 4.52 
 
 3.80 
 
 3.56 
 
 3.03 
 
 1.52 
 
 30 
 
 1.22 
 
 6.86 
 
 5.75 
 
 5.47 
 
 4.65 
 
 1.32 
 
 1.45 
 
 4.37 
 
 3.67 
 
 3.44 
 
 2.93 
 
 1.65 
 
 31 
 
 1.30 
 
 6.64 
 
 5.57 
 
 5.29 
 
 4.50 
 
 1.41 
 
 1.55 
 
 4.23 
 
 3.56 
 
 3.33 
 
 2.84 
 
 1.77 
 
 32 
 
 1.33 
 
 6.43 
 
 5.39 
 
 5.13 
 
 4.36 
 
 1.50 
 
 1 65 
 
 4.10 
 
 3.45 
 
 3 22 
 
 2.751.90 
 
 33 
 
 1.46 
 
 6.24 
 
 5.23 
 
 4.97 
 
 4.23 
 
 1.60 1.76 
 
 II 
 
 3.97 
 
 3.34 
 
 3.13 
 
 2.66 
 
 2.03 
 
TABLE OF SAFE LOADS. 
 
 51 
 
 PENCOYD 
 
 8" and 7" 
 
 6" and 5" 
 
 O 
 
 BEAMS. 
 
 Maximum and minimum sections of each shape. 
 
 Greatest safe load in Net Tons evenly distributed, including beam itself. 
 Deflections in inches corresponding to given loads for each size of beam. 
 For a load in middle of beam allow one-half the tabular figures. 
 Deflection for latter load will be -*o~ of the tabular deflection. 
 
 CHART 
 NUMBER. 
 
 i 
 
 64 
 
 64 
 
 65 
 
 65 
 
 A 
 
 i 
 
 < 
 
 X 
 < 
 
 66 
 
 66 
 
 67 
 
 67 
 
 4 
 
 SIZE OF 
 BEAM 
 
 w 
 
 8" 
 
 8" 
 
 7" 
 
 7" 
 
 M 
 
 w 
 
 M 
 
 6" 
 
 6" 
 
 5" 
 
 5" 
 
 m 
 
 M 
 
 IN IN*. 
 
 So 
 
 
 
 
 
 _ 
 
 b 
 
 
 
 
 
 io 
 
 WT. PER 
 
 a 
 
 
 
 
 ff 
 
 6S 
 
 
 
 
 
 K 
 
 YD. IN 
 
 
 84 
 
 61 
 
 72 
 
 52 
 
 O 
 
 o 
 
 57 
 
 42 
 
 46 
 
 34 
 
 g 
 
 LBS. 
 
 * 
 
 
 
 
 
 m 
 
 
 
 
 
 
 3B 
 
 MOM. OF 
 INERTIA. 
 
 o 
 
 70.5 
 
 57.7 
 
 42.6 
 
 34.4 
 
 I 
 
 ECTION 
 
 26.5 
 
 22.0 
 
 14.5 
 
 12.0 
 
 55 
 O 
 
 
 ft 
 
 GREATEST SAFE LOAD. 
 
 1 
 
 U 
 
 ft 
 
 GREATEST SAFE LOAD. 
 
 M 
 ft 
 
 6 
 
 .07 
 
 19.53 
 
 11.22 
 
 9.43 
 
 7.63 
 
 .08 
 
 .10 
 
 6.87 
 
 5.70 
 
 4.53 
 
 3.73 
 
 .12 
 
 7 
 
 .10 
 
 in. 74 
 
 9.61 
 
 8.09 
 
 6.54 
 
 .11 
 
 .13 
 
 5.89 
 
 4.89 
 
 3.89 
 
 3.20 
 
 .16 
 
 8 
 
 .13 
 
 14.65 
 
 8.41 
 
 7.07 
 
 5.73 
 
 .15 
 
 .17 
 
 5.15 
 
 4.27 
 
 3.40 
 
 2.80 
 
 .21 
 
 
 .16 
 
 13.02 
 
 7.48 
 
 6.29 
 
 5.09 
 
 .19 
 
 .22 
 
 4.58 
 
 
 3.02 
 
 2.49 
 
 .26 
 
 &q 10 
 
 .20 
 
 11.72 
 
 6.73 
 
 5.66 
 
 4.58 
 
 .23 
 
 27 
 
 4.12 
 
 3.42 
 
 2.72 
 
 2.24 
 
 .32 
 
 fe 11 
 
 24 
 
 10.65 
 
 6.12 
 
 5.15 
 
 4.16 
 
 .28 
 
 .32 
 
 3.75 
 
 3.11 
 
 -2-47 
 
 "T04 
 
 -39 
 
 
 .29 
 
 9.77 
 
 5.61 
 
 4.72 
 
 3.82 
 
 .33 
 
 .38 
 
 3.43 
 
 2.85 
 
 2.27 
 
 1.87 
 
 .46 
 
 B 13 
 
 .34 
 
 9.01 
 
 5.18 
 
 4.35 
 
 3.52 
 
 .38 
 
 "45 
 
 "Or 
 
 2.63 
 
 2.09 
 
 1.72 
 
 .54 
 
 5 14 
 
 .39 
 
 8.37 
 
 4.81 
 
 4.04 
 
 3.27 
 
 .45 
 
 .52 
 
 2.94 
 
 2.44 
 
 1.94 
 
 1.60 
 
 .63 
 
 eu 15 
 
 .45 
 
 7.81 
 
 4.49 
 
 -3T7 
 
 "Tos 
 
 T2 
 
 .60 
 
 2.75 
 
 2.28 
 
 1.81 
 
 .49 
 
 .72 
 
 16 
 
 .51 
 
 7.33 
 
 4.21 
 
 3.54 
 
 2.86 
 
 .59 
 
 .69 
 
 2.57 
 
 2.14 
 
 1.70 
 
 1.40 
 
 82 
 
 &. 17 
 
 "58 
 
 6.89 
 
 "^96 
 
 3.33 
 
 2.69 
 
 .67 
 
 .78 
 
 2.42 
 
 2.01 
 
 1.60 
 
 .32 
 
 .93 
 
 C 
 
 
 
 
 
 
 
 
 
 
 
 
 
 18 
 
 .65 
 
 6.51 
 
 3.74 
 
 3.14 
 
 2.54 
 
 .75 
 
 .87 
 
 2.29 
 
 1.90 
 
 .51 
 
 .24 
 
 1.04 
 
 g 19 
 
 .72 
 
 6.17 
 
 3.54 
 
 2.98 
 
 2.41 
 
 .83 
 
 .97 
 
 2.17 
 
 1.80 
 
 .43 
 
 .18 
 
 1.16 
 
 pO 
 
 .80 
 
 5.86 
 
 3.36 
 
 2.83 
 
 2.29 
 
 .92 
 
 1.07 
 
 2.06 
 
 1.71 
 
 .36 
 
 .12 
 
 1.29 
 
 
 .88 
 
 5.58 
 
 3.20 
 
 2.69 
 
 2.18 
 
 1.01 
 
 1.18 
 
 1.96 
 
 1.63 
 
 .30 
 
 .07 
 
 1.42 
 
 Cd 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 22 
 
 .97 
 
 5.33 
 
 3.06 
 
 2.57 
 
 2.08 
 
 1.11 
 
 1.29 
 
 1.87 
 
 1.55 
 
 .24 
 
 1.02 
 
 1.56 
 
 23 
 
 1.06 
 
 5.10 
 
 2.9.3 
 
 2.46 
 
 .99 
 
 1.22 
 
 1.41 
 
 1.79 
 
 1.49 
 
 .18 
 
 .97 
 
 1.70 
 
 24 
 
 1.16 
 
 4.88 
 
 2.80 
 
 2.36 
 
 91 
 
 1.34 
 
 1.54' 1.72 
 
 1.42 
 
 .13 
 
 .93 
 
 1.85 
 
 25 
 
 1.26 
 
 4.69 
 
 2.69 
 
 2.26 
 
 .83 
 
 1.45 
 
 1.67 
 
 1.65 
 
 1.37 
 
 .09 
 
 .90 
 
 2.01 
 
 26 
 
 1 36 
 
 4.51 
 
 2.59 
 
 2.18 
 
 .76 
 
 1.571 
 
 1.81 
 
 1.58 
 
 1.32 
 
 1.05 
 
 .86 
 
 2.18 
 
 27 
 
 1.46 
 
 4.34 
 
 2.49 
 
 2.10 
 
 .701.69 
 
 1.95 
 
 1.53! 1.27 
 
 1 01 
 
 .83 
 
 2 36 
 
 28 
 
 1.57 
 
 4.19 
 
 2.40 
 
 2 02 
 
 .641.82 
 
 2.10 
 
 1.47 
 
 1.22 .97 
 
 .80 
 
 2 54 
 
 29 
 
 1.68 
 
 4.04 
 
 2.32 
 
 1.95 
 
 .58 
 
 1.95 
 
 2.25 
 
 1.42 
 
 1.18 
 
 .94 
 
 
 2.73 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
52 WROUGHT IRON AND STEEL. 
 
 IRON FLOOR BEAMS. 
 
 When I beams are used as floor joists or girders, the spacing 
 and proper size of beams depends on the amount and character 
 of the loads, as well as the distance to be spanned. Not only the 
 positive strength, but the elasticity or amount of deflection per- 
 missible must be considered. 
 
 A heavy load per unit of area may not require as strong a 
 floor as that necessary for a lighter one, if the latter be liable to 
 sudden application, especially if accompanied with impact, 
 while the normal state of the heavier load is quiescence, or slow 
 and even change. It would require a special treatise to describe 
 the subject, and those lacking experience are referred to the 
 published literature which is now very ample and complete. It 
 has been demonstrated that the greatest mass of men that can 
 be packed on any floor will not exceed in weight 80 Ibs. per 
 square foot. The weight of the iron beams will depend on the 
 span, for which see a general rule farther on. If brick arches 
 are Inid between the beams, the weight of a 4" course of brick, 
 including the concrete filling, will be about 50 Ibs. per square foot. 
 
 Within the limits of length of span in which rolled I beams 
 can be used, it may be assumed that a floor is safe to sustain the 
 greatest possible load of men, when the following loading does 
 not exhibit a greater bending stress on the beam than that de- 
 noted in the tables, under the head of " Greatest Safe Load Dis- 
 tributed," pages 40-51. 
 
 I Beam joists with wooden floor 100 Ibs. per square foot. 
 Wooden floor and plastered ceilings =110 " " " " 
 4" brick arches and concrete filling 150 " " " " 
 
 These figures represent the total weight of floor itself and the 
 imposed load. 
 
 When the floor beams are subject to the action of moving 
 loads, it is necessary to make allowance for a greater nominal 
 weight than actually may occur, especially if the span is long 
 in proportion to the depth of the beam. If the beams are too 
 light, the resulting tremor and vibration will be a source of dis- 
 comfort to the user, if not of weakness to the structure. The 
 same results are obtained by assuming either a higher nominal 
 load per unit of area than actually can occur, or adopting a 
 higher factor of safety, than given in our tables, for the actual 
 
WEIGHT OF IRON IN FLOOB BEAMS. 53 
 
 loads. Floors proportioned as follows for given purposes will be 
 found satisfactory. The weight of the material may be included 
 in the figures. 
 
 CHARACTER OP FLOOR. 
 
 LOAD PER SQ. FT. 
 
 Very lightest floors, plank covering . 
 
 100 Ibs 
 
 Very lightest floors, brick arches 
 
 150 " 
 
 Light warehouse floors 
 
 9QO " 
 
 Halls of audience 
 
 200 " 
 
 Warehouses in which heavy pieces are moved. . 
 Shop floors for light machinery 
 
 250 " 
 250 " 
 
 Shop floors for heavy machinery. 
 
 300 to 500 Ibs 
 
 
 
 GENERAL RULE FOR THE WEIGHT OF IRON IN 
 FLOOR BEAMS. 
 
 When the standard section of any size of beam is used, 
 the weight of iron obtained by the following rule will be 
 found to approximate closely to the actual amount required: 
 " Square of span in feet divided by 5 times the depth of the beam 
 in inches, equals the pounds of iron in the beams per square 
 
 foot of floor "f- 8 ^ 2 ,-, = Ibs 
 \5 x depth 
 
 This is for a load of 150 Ibs. per square foot, and the beams 
 strained up to the maximum safe limit as given in the tables. 
 
 With the same space the weight of the beams will vary directly 
 as the load varies, consequently the weight of iron for any other 
 required loading per square foot can be obtained by proportion 
 from above rule. Example. A floor of 20 feet span is subject 
 to a load of 150 Ibs. per square foot. The weight of the iron 
 
 20 2 
 beams will be F~^TK =5.33 Ibs. per square foot of floor, if 15" 
 
 2Q2 
 
 Beams are used, or if 12" Beams are used = ^ = 6.66 Ibs. per 
 
 square foot. To these figures add the weight of ends built into 
 the wall, which should be from 6" to 12" at each end, according 
 to the span, etc. If the load to be sustained is 250 Ibs. per sq. 
 foot, on 15" I beams the necessary weight becomes as 150 : 250 :: 
 5.33 Ibs. : 8.88 Ibs. per square foot. 
 
64 WKOUGHT IKON AND STEEL. 
 
 This rule applies only to the minimum section of any I beam. 
 If the section is increased, the weight of iron required will also 
 increase. By the above it will be observed that the deeper the 
 beam used the less the amount of iron required, and such is the 
 case as a general rule. But for short spans the use of the deep- 
 est beams might require too wide a spacing to suit the covering 
 of the floor. Then the best economy requires the adoption of a 
 shallower and lighter beam. For brick arches for fire-proof 
 floors it is usual to limit the rise or spring from 3 to 6 inches, in 
 order to build in and conceal the tie rods, which should not be 
 much if any above the center of the beam. For such flat arches 
 the spacing of the beams should not exceed 6 feet, and if a 
 single 4" course of brick is used, it is safest not to exceed 5 feet 
 separation. Of course for arches of more rise and for other 
 special purposes than indicated above, no such limitation is 
 necessary. 
 
 SPACING OF FLOOR BEAMS. 
 
 The following rule gives the greatest distance apart that floor- 
 beams can be placed to support safely any given load per square 
 foot. Multiply the length of span in feet by the load in Ibs. per 
 square foot. Find iu the table, page 40, the safe load in Ibs. for 
 a beam of the size and length desirable to use. Divide this safe 
 load by the product first found, and the quotient is the greatest 
 distance in feet that the beams ought to be placed, center to 
 
 center. Or Distance = -. w = Ibs. per square foot. 
 
 L = length of span in feet. 
 
 Example. A floor of 20 feet span with its full load will weigh 
 150 Ibs. per square foot. Different sizes of beams may be safely 
 spaced as far apart as follows : For 15" 145 Ib. I Beams 
 
 80x150 = 10 ' 8 feet center to center - For 13 " 12 lb - l beams 
 
 The tables on pages 56-62 show the greatest distance apart, 
 center to center, that beams should be placed for a loading (in- 
 cluding the weight of the floor itself) of 100, 150, 200, or 250 Ibs. 
 per square foot. 
 
SPACING OF FLOOR BEAMS. 55 
 
 The deflections of the beams which are given .in the tables 
 will be uniform for beams of the given spans so long as the spac- 
 ing is proportioned according to the table. 
 
 In the case of plastered ceilings or other circumstances where 
 undue deflection might be injurious, it is considered good prac- 
 tice to limit the deflection to about T ,- (T of the span. When 
 the deflections exceed this amount, the corresponding loads in 
 the table are printed in small figures. When the deflection is 
 below this amount, the figures for the loads are in larger print. 
 The proper spacing of beams for any load is inversely propor- 
 tioned to the loads. Consequently the proper distance apart for 
 beams for any load per square foot can be easily obtained di- 
 rectly from the table as well as by the rule previously given. 
 
 Rule. Multiply the distance given in the table by 150 and 
 divide by the number of Ibs. per square foot required to be sus- 
 tained. The quotient will be the greatest distance apart for the 
 beams. 
 
 Example. What is the greatest distance apart 8" 65 Ibs, I 
 beams can be placed to support safely a load of 220 Ibs. per 
 square foot, the beams having a clear span of 18 feet ? By the 
 
 table the spacing for 150 Ibs. per foot is 3.3 feet ~* n 1 ^ > 2.25 
 
 /w 
 
 feet, the distance required. 
 
 [UNIVERSITY 
 
56 
 
 WROUGHT IRON AND STEEL. 
 
 PENCOYD 
 
 o 
 
 DECK BEAMS. 
 
 Greatest distance between floor beams so that the bending stress on the 
 beam will not exceed its maximum safe load. 
 
 1 
 
 
 
 | 
 
 of 
 
 LENGTH OP SPAN IN FEET. 
 
 1 
 
 fc 
 
 if 
 
 8| 
 
 O" -! 
 ** 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 g 
 
 o g 
 
 H ni 
 
 P* ^ 
 
 
 
 
 
 
 
 es 
 
 gs 
 
 i 
 
 o 
 
 ft 
 < 
 
 DISTANCE BETWEEN CENTRES OP 
 
 o 
 
 02 
 
 1 
 
 3 
 
 BEAMS IN FEET. 
 
 
 
 
 100 
 
 
 
 17.6 
 
 13.5 
 
 10.7 
 
 8.6 
 
 
 
 
 150 
 
 
 
 11.7 
 
 9.0 
 
 7.1 
 
 5.8 
 
 60 
 
 12 
 
 104 
 
 200 
 
 
 
 8.8 
 
 6.7 
 
 5.3 
 
 4.3 
 
 
 
 
 250 
 
 
 
 7.0 
 
 5.4 
 
 4.3 
 
 3.5 
 
 
 Deflection 
 
 in Inches. 
 
 i 
 
 
 .28 
 
 .34 
 
 .44 
 
 .54 
 
 
 
 
 100 
 
 
 19.3 
 
 14.2 
 
 10.9 
 
 8.6 
 
 7.0 
 
 
 
 
 150 
 
 
 12.9 
 
 9.5 
 
 7.2 
 
 5.7 
 
 4.6 
 
 61 
 
 11 
 
 91 
 
 20 
 
 
 9.7 
 
 7.1 
 
 5.4 
 
 4.3 
 
 3.5 
 
 
 
 
 250 
 
 
 7.7 
 
 5.7 
 
 4.3 
 
 3.4 
 
 2.8 
 
 
 Deflection 
 
 in Inches. 
 
 
 
 .21 
 
 .29 
 
 .37 
 
 .46 
 
 .58 
 
 
 
 
 100 
 
 2-2.1 
 
 15.3 
 
 11.3 
 
 8.6 
 
 6.8 
 
 5.5 
 
 
 
 
 150 
 
 14.7 
 
 10.2 
 
 7.5 
 
 5.7 
 
 4.5 
 
 3.7 
 
 62 
 
 10 
 
 80 
 
 200 
 
 11.0 
 
 
 5.6 
 
 4.3 
 
 3.4 
 
 2.8 
 
 
 
 
 250 
 
 8.8 
 
 0J 
 
 4.5 
 
 3.4 
 
 2.7 
 
 2.2 
 
 
 Deflection 
 
 in Inches. 
 
 
 .16 
 
 .23 
 
 .32 
 
 .41 
 
 .52 
 
 .64 
 
 
 
 
 100 
 
 17.6 
 
 12.2 
 
 9.0 
 
 6.9 
 
 5.4 
 
 4-4 
 
 
 
 
 150 
 
 11.7 
 
 8.1 
 
 6.0 
 
 4.6 
 
 3.6 
 
 2-9 
 
 63 
 
 9 
 
 72 
 
 200 
 
 8.8 
 
 6.1 
 
 4.5 
 
 3.4 
 
 2.7 
 
 2-2 
 
 
 
 
 250 
 
 7.0 
 
 4.9 
 
 3.6 
 
 2.7 
 
 2.2 
 
 1 
 
 
 Deflection 
 
 in Inches. 
 
 
 .18 
 
 .26 
 
 .35 
 
 .46 
 
 .58 
 
 71 
 
 
 
 
 100 
 
 13.4 
 
 9.3 
 
 6.9 
 
 5.2 
 
 4-1 
 
 3-4 
 
 
 
 
 150 
 
 9.0 
 
 6.2 
 
 4.6 
 
 3.5 
 
 2-8 
 
 2-2 
 
 64 
 
 8 
 
 61 
 
 200 
 
 6.7 
 
 4.7 
 
 3.4 
 
 2.6 
 
 2- 1 
 
 1 -7 
 
 
 
 
 250 
 
 5.4 
 
 3.7 
 
 2.7 
 
 2.1 
 
 1 -7 
 
 1 -3 
 
 
 Deflection 
 
 in Inches. 
 
 
 
 .20 
 
 .29 
 
 .b9 
 
 .51 
 
 B5 
 
 to 
 
 
 
 
 100 
 
 9.2 
 
 6.4 
 
 4.7 
 
 3- 
 
 2-8 
 
 2 3 
 
 
 
 
 150 
 
 6.1 
 
 4.2 
 
 3.1 
 
 2- 
 
 1 -9 
 
 1 -5 
 
 65 
 
 7 
 
 52 
 
 200 
 
 4.6 
 
 3.2 
 
 2.3 
 
 1 
 
 1 -4 
 
 J-l 
 
 
 
 
 250 
 
 3.7 
 
 2.5 
 
 1.9 
 
 1- 
 
 1-1 
 
 ' 
 
 
 Deflection 
 
 in Inches. 
 
 
 .23 
 
 .33 
 
 .45 
 
 & 
 
 75 
 
 92 
 
 
 
 
 100 
 
 6.8 
 
 4.7 
 
 3- 
 
 2- 
 
 2-1 
 
 1 -7 
 
 
 
 
 150 
 
 4.5 
 
 3.2 
 
 2- 
 
 I- 
 
 1-1 
 
 1 1 
 
 66 
 
 6 
 
 42 
 
 200 
 
 3.4 
 
 2.4 
 
 1- 
 
 1- 
 
 1-1 
 
 9 
 
 
 
 
 250 
 
 2.7 
 
 1.9 
 
 1 
 
 1 
 
 8 
 
 7 
 
 
 Deflection 
 
 in Inches. 
 
 
 .27 
 
 .39 
 
 f> 
 
 - 6 
 
 87 
 
 1 -07 
 
 
 
 
 100 
 
 4.5 
 
 3-1 
 
 2- 
 
 ] 
 
 
 
 
 
 
 150 
 
 3.0 
 
 2-1 
 
 I- 
 
 1 
 
 
 
 67 
 
 5 
 
 34 
 
 200 
 
 2.2 
 
 1 
 
 1- 
 
 
 
 
 
 
 
 250 
 
 1.8 
 
 1-2 
 
 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 .32 
 
 46 
 
 6 
 
 8 
 
 
 
FLOOR BEAMS. 
 
 57 
 
 PENCOYD 
 
 :Q DECK 
 
 BEAMS. 
 
 Figures in small type denote that the beams so placed will deflect more 
 than J;- of an inch for each foot of span. 
 
 LENGTH OF SPAN IN FEET. 
 
 B 
 
 O 
 
 j. 
 
 I 
 
 
 8^. 
 
 H 
 
 ft 
 
 B| 
 
 fe g 
 
 H 
 
 H 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 
 
 
 
 
 
 ^h^ 
 
 E-- 1 
 
 a 
 
 * 
 
 g 
 
 
 DISTANCE BETWEEN CENTRES OF 
 
 ^ 
 
 o 
 
 ~ M 
 
 s 
 
 BEAMS IN FEET. 
 
 o 
 
 m 
 
 
 
 7.1 
 
 6.0 
 
 5- 
 
 4-4 
 
 3-8 
 
 3-4 
 
 100 
 
 
 
 
 4.8 
 
 4.0 
 
 3- 
 
 2-9 
 
 2- 
 
 2-2 
 
 150 
 
 
 
 
 3.6 
 
 3.0 
 
 2- 
 
 2-2 
 
 1 
 
 1 -7 
 
 200 
 
 104 
 
 12 
 
 60 
 
 2.9 
 
 2.4 
 
 2- 
 
 ] -8 
 
 1 
 
 1-3 
 
 250 
 
 
 
 
 .65 
 
 .78 
 
 9 
 
 1-00 
 
 1-2 
 
 1-33 
 
 
 Deflection 
 
 in Inches. 
 
 
 5.8 
 
 4 -8 
 
 4- 
 
 3-6 
 
 3- 
 
 2-7 
 
 100 
 
 
 
 
 3.8 
 o ft 
 
 3-2 
 
 2- 
 
 2-4 
 
 2- 
 
 1 8 
 
 150 
 
 
 
 el 
 
 u.y 
 2.3 
 
 1 -9 
 
 1-6 
 
 1-4 
 
 1- 
 
 1-1 
 
 200 
 250 
 
 91 
 
 11 
 
 ol 
 
 .71 
 
 84 
 
 99 
 
 1-15 
 
 1 ' 3 
 
 1-50 
 
 
 Deflection 
 
 in Inches. 
 
 
 3-0 
 
 2-6 
 
 2-2 
 
 ] 
 
 j. 
 
 
 100 
 150 
 
 
 
 
 2-3 
 
 1-9 
 
 1 I) 
 
 1 -4 
 
 1- 
 
 
 2ori 
 
 80 
 
 10 
 
 62 
 
 1 -8 
 
 1 -5 
 
 1-3 
 
 1 1 
 
 1 
 
 
 250 
 
 
 
 
 78 
 
 93 
 
 1-09 
 
 1-26 
 
 1 -4 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 3-6 
 
 3-1 
 
 2-6 
 
 2-2 
 
 
 
 100 
 
 
 
 
 2-4 
 
 2-0 
 
 1-7 
 
 1-5 
 
 
 
 150 
 
 
 
 
 1 ti 
 
 1-5 
 
 1 -3 
 
 1 1 
 
 
 
 200 
 
 72 
 
 9 
 
 63 
 
 J-5 
 
 1-2 
 
 1 -0 
 
 9 
 
 
 
 250 
 
 
 
 * 
 
 66 
 
 1-03 
 
 1-21 
 
 1-40 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 2-8 
 
 2-3 
 
 2-0 
 
 
 
 
 100 
 
 
 
 
 1 -9 
 
 1-R 
 
 1-3 
 
 
 
 
 150 
 
 
 
 
 1-4 
 
 1-2 
 
 1 -0 
 
 
 
 
 200 
 
 61 
 
 8 
 
 64 
 
 1-1 
 
 9 
 
 8 
 
 
 
 
 250 
 
 
 
 
 97 
 
 1-16 
 
 1-36 
 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 1-9 
 
 
 
 
 
 
 100 
 
 
 
 
 1-3 
 
 
 
 
 
 
 150 
 
 
 
 
 9 
 
 
 
 
 
 
 200 
 
 52 
 
 7 
 
 65 
 
 8 
 
 
 
 
 
 
 250 
 
 
 
 
 I'lO 
 
 
 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 150 
 
 
 
 
 
 
 
 
 
 
 200 
 
 42 
 
 6 
 
 66 
 
 
 
 
 
 
 
 250 
 
 
 
 
 
 
 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 150 
 
 
 
 
 
 
 
 
 
 
 200 
 
 34 
 
 5 
 
 67 
 
 
 
 
 
 
 
 250 
 
 
 
 
 
 
 
 
 
 
 
 Deflection 
 
 in Inches. 
 
 
 
 
 
 
 
 
 
58 
 
 WROUGHT IRON AND STEEL. 
 
 PENCOYD 
 
 BEAMS. 
 
 Greatest distances between centres of floor beams, so that the bending 
 stress on the beam will not exceed its maximum safe load. 
 
 CHART NUMBER. 
 
 g 
 
 Sis 
 
 W pq 
 
 &1 
 
 H M 
 
 
 OD 
 
 WEIGHT PER YARD, 
 
 LBS. 
 
 LOAD PER SQ. FT. 
 OF FLOOR, 
 
 LBS. 
 
 LENGTH OF SPAN IN FEET. 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 DISTANCE BETWEEN CENTRES OF 
 BEAMS IN FEET. 
 
 1 
 2 
 3 
 
 4 
 
 
 
 5 
 t% 
 
 6 
 
 15 
 Deflection 
 
 15 
 Deflection 
 
 12 
 Deflection 
 
 12 
 Deflection 
 
 10* 
 Deflection 
 
 201 
 
 Deflection 
 
 1C* 
 Deflection 
 
 200 
 in Inches. 
 
 145 
 in Inches. 
 
 168 
 in Inches. 
 
 120 
 in Inches. 
 
 134 
 in Inches. 
 
 108 
 in Inches. 
 
 89 
 in Inches 
 
 100 
 150 
 200 
 250 
 
 
 
 
 33.1 
 22.1 
 16.6 
 13.3 
 .27 
 
 25.3 
 16.9 
 12.7 
 10.1 
 .27 
 
 22.6 
 15.1 
 11.5 
 9.0 
 .34 
 
 16.6 
 11.1 
 8.3 
 <i.6 
 .34 
 
 16.8 
 11.2 
 8.4 
 6.7 
 .39 
 
 13.6 
 9.1 
 6.8 
 5.4 
 .39 
 
 11.3 
 7.5 
 5.6 
 4.5 
 .39 
 
 26.2 
 17.5 
 13.1 
 10.5 
 .34 
 
 20.0 
 13.3 
 10.0 
 8.0 
 .34 
 
 17.9 
 11.9 
 8.9 
 7.1 
 .43 
 
 13.1 
 8.7 
 6.5 
 5. '2 
 .43 
 
 13.3 
 8.9 
 6.6 
 5.3 
 .49 
 
 10.7 
 7.1 
 5.4 
 4.3 
 .49 
 
 8.9 
 5.9 
 4.4 
 3.5 
 .49 
 
 21.2 
 14.1 
 10.6 
 8.5 
 .42 
 
 16.2 
 10.8 
 8.1 
 6.5 
 .42 
 
 14.5 
 9.6 
 7.2 
 5.8 
 .53 
 
 10.6 
 7.1 
 5.3 
 4.2 
 .53 
 
 10.7 
 7.1 
 5.4 
 4.3 
 .61 
 
 8.7 
 5.8 
 4.3 
 3.4 
 .61 
 
 7.2 
 4.8 
 3.6 
 2.9 
 .61 
 
 100 
 150 
 200 
 250 
 
 
 
 
 100 
 150 
 200 
 250 
 
 
 
 29.5 
 19.7 
 14.8 
 11.8 
 .26 
 
 21.7 
 
 14!4 
 10.8 
 8.7 
 .26 
 
 2J.9 
 14.6 
 11.0 
 8.8 
 .30 
 
 17.7 
 11.8 
 8.9 
 7.1 
 .30 
 
 14.7 
 9.8 
 7.4 
 5.9 
 .30 
 
 100 
 150 
 200 
 250 
 
 
 
 100 
 150 
 
 200 
 250 
 
 
 29.8 
 19.9 
 14.9 
 11.9 
 .22 
 
 24.1 
 16.1 
 12.1 
 9.7 
 .22 
 
 20.0 
 13.3 
 10.0 
 8.0 
 .22 
 
 100 
 130 
 200 
 250 
 
 
 100 
 150 
 200 
 250 
 
 
 
 
FLOOK BEAMS. 
 
 PENCOYD 
 
 
 BEAMS. 
 
 Figures in small type denote that the beams so placed will deflect more 
 than :j\ r of an inch for each foot of span. 
 
 LENGTH OF SPAN IN FEET. 
 
 LOAD PER SQ. FT. 
 OF FLOOR, 
 LBS. 
 
 WEIGHT PER YARD, 
 LBS. 
 
 M 
 < . 
 
 ! 
 
 63 
 
 $5 
 
 O2 
 
 CHART NUMBER. 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 DISTANCE BETWEEN CENTRES OF 
 BEAMS IN FEKT. 
 
 17.5 
 11.7 
 8.8 
 7.0 
 .51 
 
 13.4 
 8.9 
 6.7 
 5.4 
 .51 
 
 12.0 
 8.0 
 6.0 
 4.8 
 .64 
 
 8.8 
 5.8 
 4.4 
 3.5 
 .64 
 
 14.7 
 9.8 
 7.4 
 5.9 
 .61 
 
 11.3 
 7.5 
 5.6 
 4.5 
 .61 
 
 10.0 
 6.7 
 5.0 
 4.0 
 .77 
 
 7.4 
 
 4.9 
 
 12.5 
 8.4 
 6.3 
 5.0 
 .11 
 
 9.6 
 6.4 
 4.8 
 3.9 
 .72 
 
 8- 
 5-7 
 4-3 
 3-4 
 
 90 
 
 -3 
 4-2 
 
 10.8 
 7.2 
 5.4 
 4.3 
 .83 
 
 8.3 
 5.5 
 4.1 
 3.4 
 .83 
 
 7-4 
 4-9 
 3-7 
 3-0 
 1 -05 
 
 5-4 
 3-6 
 
 9.4 
 6.3 
 4.7 
 3.8 
 .95 
 
 7.2 
 
 4.8 
 3.6 
 2.9 
 .95 
 
 B- 
 4- 
 
 2- 
 1 -2 
 
 4-7 
 
 8- 
 5- 
 4 
 
 3. 
 
 1 -0 
 
 6- 
 4 
 
 2- 
 1 -0 
 
 5- 
 3- 
 2- 
 
 
 1-3 
 
 4- 
 2- 
 
 100 
 150 
 2CO 
 250 
 
 100 
 150 
 200 
 250 
 
 200 
 Deflection 
 
 145 
 Deflection 
 
 168 
 Deflection 
 
 120 
 Deflection 
 
 134 
 Reflection 
 
 108 
 Reflection 
 
 89 
 Deflection 
 
 15 
 
 in Inches 
 
 15 
 in Inches 
 
 12 
 in Inches 
 
 12 
 in Inches. 
 
 1C1 
 in Inches. 
 
 ICi 
 in Inches. 
 
 1C* 
 n Inches. 
 
 1 
 2 
 3 
 4 
 5 
 
 ei 
 
 6 
 
 100 
 150 
 200 
 250 
 
 100 
 150 
 2(0 
 250 
 
 2.9 
 .77 
 
 2-5 
 30 
 
 2-2 
 1-05 
 
 1 -9 
 1-20 
 
 1-36 
 
 4-a 
 
 100 
 
 4.4 
 
 3-5 
 74 
 
 7-2 
 4-8 
 3-6 
 2-9 
 
 3-7 
 3-0 
 
 88 
 
 3-2 
 2-6 
 1'03 
 
 2-7 
 2-3 
 1-19 
 
 2-4 
 1 -9 
 1-37 
 
 2- 
 1 5 
 
 150 
 200 
 250 
 
 100 
 150 
 200 
 250 
 
 100 
 150 
 200 
 250 
 
 4*0 
 
 3-0 
 2-4 
 
 3-4 
 2-6 
 2-1 
 
 2-9 
 2-2 
 
 1 -8 
 
 2-6 
 1 -9 
 1-5 
 
 2- 
 1- 
 
 1- 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 1'57 
 
 2-4 
 74 
 
 2-0 
 
 88 
 
 1-7 
 
 1-03 
 
 1 '4 
 1-19 
 
 1 '3 
 1-37 
 
60 
 
 WEOUGHT IKON AND STEEL. 
 
 PENCOYD 
 
 BEAMS. 
 
 Greatest distances between centres of floor beams, so that the bending 
 stress on the beam will nut exceed its maximum safe load. 
 
 i 
 
 g 
 % 
 
 1 
 
 6 
 
 LENGTH OF SPAN IN FEET. 
 
 
 
 la 
 
 |y 
 
 * 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 j^ 
 
 & s 
 
 SQ 
 
 S j pfl 
 
 
 
 
 
 
 
 S 
 
 ^ 
 
 m 1 " 
 
 fcSe, ^ 
 
 
 
 
 
 
 
 
 a 
 
 s 
 
 2 
 
 < O 
 
 DISTANCE BETWEEN CENTRES OF 
 
 a 
 
 
 
 
 S 
 
 BEAMS IN FEET. 
 
 
 
 
 100 
 
 32.4 
 
 29.5 
 
 16.5 
 
 12.7 
 
 10.0 
 
 8.1 
 
 
 
 
 150 
 
 21.6 
 
 15.0 
 
 11 
 
 8.4 
 
 6.7 
 
 5.4 
 
 7 
 
 10 
 
 112 
 
 200 
 
 16.2 
 
 11.3 
 
 8.3 
 
 6.3 
 
 5.0 
 
 4.1 
 
 
 Deflection 
 
 in Inches. 
 
 250 
 
 13.0 
 .16 
 
 9.0 
 .23 
 
 6.6 
 .31 
 
 5.1 
 .41 
 
 4.0 
 .52 
 
 3.2 
 .C4 
 
 
 
 
 100 
 
 27.7 
 
 19.2 
 
 14.1 
 
 10.8 
 
 8.5 
 
 6.9 
 
 
 
 
 150 
 
 18.4 
 
 12.8 
 
 9.4 
 
 7.2 
 
 5.7 
 
 4.6 
 
 8 
 
 10 
 
 90 
 
 200 
 
 13.8 
 
 9.6 
 
 7.1 
 
 5.4 
 
 4.3 
 
 3.5 
 
 
 
 
 250 
 
 11.1 
 
 7.7 
 
 5.6 
 
 4.3 
 
 3.4 
 
 2.8 
 
 
 Deflection in Inches . 
 
 
 .16 
 
 .23 
 
 .31 
 
 .41 
 
 .52 
 
 .64 
 
 
 
 
 100 
 
 24.6 
 
 17.1 
 
 12.6 
 
 9.6 
 
 7.6 
 
 6-2 
 
 
 
 
 150 
 
 16.4 
 
 11.4 
 
 8.4 
 
 6.4 
 
 5.1 
 
 4-1 
 
 9 
 
 9 
 
 90 
 
 200 
 
 12.3 
 
 8.6 
 
 6.3 
 
 4.8 
 
 3.8 
 
 3-1 
 
 
 
 
 250 
 
 9 '' 
 
 6.8 
 
 5.0 
 
 3 8 
 
 3.0 
 
 2 5 
 
 
 Deflection 
 
 in Inches. 
 
 
 .is 
 
 .26 
 
 .35 
 
 .46 
 
 .58 
 
 71 
 
 
 
 
 100 
 
 19.6 
 
 13.6 
 
 10.0 
 
 7.7 
 
 6.1 
 
 4-9 
 
 
 
 
 150 
 
 13 1 
 
 9.1 
 
 6.7 
 
 5.1 
 
 4.0 
 
 3-3 
 
 10 
 
 9 
 
 70 
 
 200 
 
 9.8 
 
 6.8 
 
 5.0 
 
 3.8 
 
 3.0 
 
 2-4 
 
 
 
 
 250 
 
 7.8 
 
 5.4 
 
 4.0 
 
 3.1 
 
 2.4 
 
 2-0 
 
 
 Deflection 
 
 in Inches. 
 
 
 .18 
 
 .26 
 
 .35 
 
 .46 
 
 .58 
 
 71 
 
 
 
 
 100 
 
 19.6 
 
 13.6 
 
 10.0 
 
 7.7 
 
 6- 
 
 4-9 
 
 
 
 
 150 
 
 13.1 
 
 9.1 
 
 6.7 
 
 5.1 
 
 4 
 
 3-3 
 
 11 
 
 8 
 
 81 
 
 200 
 
 9.8 
 
 6.8 
 
 5.0 
 
 3.8 
 
 S- 
 
 2-4 
 
 
 
 
 250 
 
 7.8 
 
 5.4 
 
 4.0 
 
 3.1 
 
 2- 
 
 2-0 
 
 
 Deflection 
 
 in Inches. 
 
 
 .20 
 
 .29 
 
 .39 
 
 .51 
 
 6 
 
 80 
 
 
 
 
 100 
 
 16.1 
 
 11.2 
 
 8.2 
 
 6.3 
 
 5- 
 
 4-0 
 
 
 
 
 150 
 
 10.7 
 
 7.5 
 
 5.5 
 
 4.2 
 
 3- 
 
 2-7 
 
 12 
 
 8 
 
 65 
 
 200 
 
 8.1 
 
 5.6 
 
 4.1 
 
 3.2 
 
 2- 
 
 2- 
 
 
 
 
 250 
 
 6.5 
 
 4.5 
 
 3.3 
 
 2.5 
 
 2- 
 
 1-6 
 
 
 Deflection 
 
 in Inches. 
 
 
 .20 
 
 .29 
 
 .39 
 
 .51 
 
 6 
 
 80 
 
 
 
 
 100 
 
 13.3 
 
 9.2 
 
 6.8 
 
 
 4- 
 
 3-3 
 
 
 
 
 150 
 
 8.8 
 
 6.1 
 
 4.5 
 
 
 2- 
 
 2-2 
 
 13 
 
 7 
 
 65 
 
 200 
 
 6.6 
 
 4.6 
 
 3.4 
 
 
 2- 
 
 1 -7 
 
 
 
 
 250 
 
 5.3 
 
 3.7 
 
 2.7 
 
 
 1- 
 
 1-3 
 
 
 Deflection 
 
 in Inches. 
 
 
 .23 
 
 .33 
 
 .44 
 
 s 
 
 7 
 
 90 
 
 
 
 
 100 
 
 11.5 
 
 8.0 
 
 5.9 
 
 
 3- 
 
 2-9 
 
 
 
 
 150 
 
 7.7 
 
 5.3 
 
 3.9 
 
 
 2- 
 
 1 -9 
 
 14 
 
 7 
 
 52 
 
 200 
 
 5.7 
 
 4.0 
 
 2.9 
 
 
 I- 
 
 1-4 
 
 
 
 
 250 
 
 4.6 
 
 3.2 
 
 2.3 
 
 
 1- 
 
 1-1 
 
 
 Deflection 
 
 in Inches. 
 
 
 .23 
 
 .33 
 
 .44 
 
 5 
 
 74 
 
 90 
 
 
 
 1 
 
 
 
 
 
 
 
FLOOB BEAMS. 
 
 61 
 
 PENCOYD 
 
 BEAMS. 
 
 Figures in small type denote that the beams so placed will deflect more 
 thau 3\ r of an inch for each foot of span. 
 
 LENGTH OP SPAN IN FEET. 
 
 Ki 
 
 o>ef 
 
 ati O 
 
 38 
 
 F 
 
 WEIGHT PER YARD, 
 LBS. 
 
 
 
 n 
 
 o| 
 
 z 
 
 OB 
 
 CHART NUMBER. 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 DISTANCE BETWEEN CENTRES OF 
 BEAMS IN FEKT. 
 
 8-7 
 4-5 
 
 6-6 
 3-7 
 
 4-8 
 3-2 
 
 4-1 
 
 2-8 
 
 3- 
 2- 
 I- 
 
 1- 
 1*4 
 
 
 100 
 150 
 200 
 250 
 
 112 
 Deflection 
 
 90 
 Deflection 
 
 90 
 Deflection 
 
 70 
 Deflection 
 
 81 
 Deflection 
 
 65 
 
 Deflection 
 
 65 
 Deflection 
 
 52 
 Deflection 
 
 10 
 in Inches. 
 
 10 
 in Inches. 
 
 9 
 
 in Inches. 
 
 9 
 in Inches. 
 
 8 
 in Inches. 
 
 8 
 in Inches. 
 
 7 
 in Inches. 
 
 7 
 in Inches. 
 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 
 2-7 
 78 
 
 2-3 
 
 92 
 
 1 -9 
 1-06 
 
 1-1 
 
 1-26 
 
 
 100 
 150 
 200 
 250 
 
 8-8 
 2-9 
 
 
 
 
 
 2-4 
 
 2-0 
 
 1-8 
 
 1- 
 
 78 
 
 92 
 
 l-O.'j 
 
 1'2 
 
 1*44 
 
 
 100 
 150 
 200 
 250 
 
 3-4 
 2-5 
 2-0 
 
 86 
 
 4-0 
 3-7 
 2-0 
 1 -6 
 
 86 
 
 4-0 
 2-7 
 2-0 
 1-6 
 
 97 
 
 3-3 
 2-2 
 1 -7 
 1-3 
 
 97 
 
 2-7 
 1-4 
 1-09 
 
 2-4 
 1-6 
 1-2 
 9 
 1-09 
 
 2-8 
 2-1 
 1-7 
 1-02 
 
 3-4 
 2-3 
 1-7 
 1-4 
 1-02 
 
 3-4 
 2-3 
 1-7 
 1-4 
 1-16 
 
 2-8 
 1-9 
 1-4 
 
 1-18 
 
 2-3 
 1 5 
 1-2 
 9 
 1-32 
 
 2-0 
 1 -3 
 1-0 
 8 
 1-32 
 
 2-4 
 
 1-8 
 1-5 
 1-21 
 
 2-9 
 2-0 
 1-4 
 1-2 
 1-21 
 
 2-9 
 1 -9 
 1-4 
 1-2 
 1-36 
 
 2-4 
 ! 6 
 1-2 
 1 -0 
 1-36 
 
 2-1 
 1-8 
 1-3 
 1-40 
 
 2-5 
 1-7 
 1*9 
 
 1-0 
 1-40 
 
 
 
 100 
 150 
 200 
 250 
 
 
 
 100 
 150 
 200 
 250 
 
 
 
 
 100 
 150 
 2UO 
 250 
 
 
 
 
 100 
 150 
 200 
 250 
 
 
 
 
 
 100 
 150 
 200 
 250 
 
 
 
 
 
 
WEOUGHT IRON AND STEEL. 
 
 PENCOYD 
 
 BEAMS. 
 
 Greatest distance between centres of floor beams so that the bending 
 stress on beam will not exceed its maximum safe load. 
 
 Figures in small type denote that the beams so placed will deflect more 
 than ^ of an inch for each foot of span. 
 
 t 
 
 m 
 p 
 fc 
 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 
 SIZE or BEAM 
 
 IN INCHES. 
 
 WEIGHT PER YARD, 
 
 LBS. 
 
 : 
 f 
 
 LENGTH OP SPAN IN FEET. 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 DISTANCE FETWEEN CENTRES OP 
 
 BEAMS IN FEET. 
 
 6 
 
 Deflection 
 
 6 
 Deflection 
 
 5 
 
 Deflection 
 
 5 
 Deflection 
 
 4 
 
 Deflection 
 
 4 
 Deflection 
 
 3 
 
 Deflection 
 
 3 
 Deflection 
 
 50 
 in Inches. 
 
 40 
 in Inches. 
 
 in Inches. 
 
 30 
 in Inches. 
 
 28 
 in Inches . 
 
 18.5 
 in Inches. 
 
 23 
 in Inches. 
 
 17 
 in Inches . 
 
 100 
 150 
 200 
 250 
 
 8.4 
 
 5.6 
 4.2 
 3.3 
 .27 
 
 7.5 
 5.0 
 3.7 
 3.0 
 .27 
 
 E.O 
 3.3 
 2.5 
 2.0 
 .32 
 
 4.7 
 3.1 
 2.3 
 1.9 
 .32 
 
 R.8 
 3.9 
 2.9 
 2.3 
 .38 
 
 5.2 
 3.5 
 2.6 
 21 
 .38 
 
 2-8 
 2- 1 
 1 -7 
 62 
 
 3-8 
 2-6 
 1 -9 
 1-5 
 52 
 
 2-2 
 1-6 
 1-3 
 
 2-9 
 1-9 
 1-5 
 1-2 
 69 
 
 1-7 
 1-3 
 1-0 
 
 H7 
 
 2-3 
 1-5 
 1 -2 
 9 
 67 
 
 1-4 
 1 -0 
 8 
 1 -07 
 
 1-9 
 1-2 
 9 
 7 
 1-07 
 
 100 
 
 rso 
 
 200 
 250 
 
 100 
 150 
 200 
 250 
 
 100 
 150 
 201) 
 250 
 
 2-3 
 
 1-7 
 
 1 3 
 
 1-0 
 
 9 
 
 1-4 
 
 46 
 
 3-2 
 2- 1 
 
 J -0 
 63 
 
 2-4 
 1 -6 
 
 8 
 82 
 
 1 -8 
 1-2 
 
 8 
 1-04 
 
 1-4 
 9 
 
 5 
 1-29 
 
 1-2 
 
 8 
 
 1-3 
 
 46 
 
 1 -0 
 
 63 
 
 7 
 82 
 
 6 
 1 -04 
 
 5 
 
 1-29 
 
 100 
 150 
 200 
 250 
 
 100 
 150 
 200 
 250 
 
 100 
 150 
 200 
 250 
 
 100 
 150 
 
 200 
 250 
 
 2-4 
 1 -8 
 1-4 
 
 1-7 
 1-2 
 1-0 
 
 1-2 
 
 9 
 
 9 
 7 
 6 
 
 7 
 6 
 4 
 
 2-4 
 
 1 -6 
 
 1-7 
 
 1-2 
 
 8 
 
 
 
 7 
 6 
 
 1-0 
 
 40 
 
 2-0 
 1 -3 
 1-0 
 8 
 63 
 
 1-8 
 1 1 
 
 8 
 
 63 
 
 1-4 
 
 7 
 6 
 
 77 
 
 .7 
 
 a 
 
 4 
 
 77 
 
 5 
 79 
 
 1-0 
 7 
 5 
 4 
 1-05 
 
 0-8 
 5 
 4 
 3 
 1 -05 
 
 4 
 
 1 -03 
 
 8 
 5 
 4 
 3 
 
 1-37 
 
 8 
 4 
 3 
 2 
 1-37 
 
 3 
 
 1-31 
 
LATERAL STRENGTH OF FLOOR BEAMS. 63 
 
 TIE RODS FOR BEAMS SUPPORTING BRICK ARCHES. 
 The horizontal thrust of Brick arches is found as follows : 
 
 1.5 Wl? 
 
 ^ = pressure in Ibs. per lineal foot of arch. 
 
 W = Load in Ibs. per square foot. 
 
 L Span of arch in feet 
 
 R = Rise in inches. 
 
 Place the tie rods as low through the webs of the beams as 
 possible, and spaced so that the pressure of arches as obtained 
 above will not produce a greater stress than 15,000 Ibs. per 
 square inch of the least section of the bolt. 
 
 Example. The beams supporting an arched brick floor are 
 five feet apart, and the rise of the arches is six inches. The to- 
 tal weight of floor and load equals 150 Ibs. per square foot. 
 
 -^?- = 937.5 Ibs. pressure per lineal foot of 
 
 arch. If one-inch screw bolts are used which have an effective 
 section of -ft- square inches. Then .6 x 15,000 = 9,000 Ibs. which 
 is the greatest load the bolt should be allowed to sustain, and 
 
 9 000 
 
 -^r = 9.6 feet = greatest distance apart of the bolts, or in 
 
 9o7.5 
 
 same manner we would find 5.3 feet, if inch tie rods are used. 
 
 Ordinarily it wiJl be found necessary to limit the spacing of 
 the tie rods to avoid excessive bending stress on the outer beams 
 of the floor, or to prevent this bending stress being transferred to 
 the walls of the building. 
 
 The ability of the outer beams to resist the horizontal bending 
 action caused by the pressure of the arches is determined as fol- 
 lows : 
 
 LATERAL STRENGTH OF FLOOR BEAMS. 
 The resistance to bending of any I Beam or Channel bar, for 
 a force acting at right angles to the web, or in the direction of 
 the flanges, 
 
 w = for I Beams - 
 
 ft T 
 
 W = f-T,, for Channels. 
 
64: WROUGHT IRON AND STEEL. 
 
 W = Safe distributed load in net tons. 
 L = Length in feet between supports. 
 F Width of flange in inches. 
 
 / = Moment of inertia, axis coincident with web, see col. 
 viii., pages 92-101. 
 
 The above gives results which have been proved by experiment 
 not to exceed one-third the ultimate strength of the beams. The 
 formulae given properly apply to beams secured at each end 
 only. If the beam is of considerable length requiring supports 
 at several points, it can be considered as continuous (see page 
 75), and the formulae become, 
 
 W = , for I Beams. 
 
 127 
 
 W = for Channels. 
 
 Example. K 9-inch 70 Ib. I Beam forming the outer support 
 for an arched brick floor has the tie rods at intervals of 6 feet. 
 What evenly distributed horizontal pressure will it safely resist ? 
 /=5.6 (see col. viii., page 92). F=4^ inches (see col. C, 
 
 page 2). Then W= 15 Q * ^_ 6 - = 3.4 tons or 1,130 Ibs. per lin- 
 eal foot of arch. 
 Knowing the amount of the load W and requiring the distance 
 
 L, Above equation becomes L? -==7-= in which W 1 = pres- 
 
 W Jf 
 
 sure or load on beam per lineal foot. 
 
 .Example. An 8" 43 Ib. channel bar forms the end support 
 for a system of brick arches having a span of 4 feet and 4 inches 
 rise. How closely ought tie rods to be placed so that the chan- 
 nels will not be overstrained ? The horizontal thrust per lineal 
 
 foot of arch = 1 ' 5 x ^ x 16 = 900 Ibs. or .45 tons. I - 2.17. 
 
 F=W*. 
 
 12 x 2.17 
 
BEAMS SUPPORTING BRICK WALLS. 
 
 65 
 
 It will generally be found that an angle bar makes a better 
 and more economical support for the arches on the side walls 
 than either an I beam or channel. 
 
 The resistance to bending of an angle is readily found by the 
 rule given on page 69. 
 
 W = - - = safe distributed load for a non-continuous 
 Li 
 
 beam. 
 
 1 4A.D 
 
 W -4-= = safe distributed load for a continuous beam. 
 Li 
 
 And as before L z = 
 
 1AAD 
 
 A being the sectional area in 
 
 square inches, and D the width or size of the angle in inches. 
 
 Applying this rule to the last example, and considering the 8" 
 channel replaced by a 4" x 4' x i" angle whose area = 3. 75 
 square inches. 
 
 1.4 x 3.75 x 4 
 
 .45 
 
 = 46 . 6 or L = 6 . 8 feet between centers 
 
 of boits. Stress on bolts 900 x 6.8 = 6,120 Ibs. To resist this 
 |" would be the proper diameter of the screw. 
 
 BEAMS SUPPORTING BRICK WALLS. 
 
 If the wall has no openings and the bricks are laid with the 
 usual bond, the prism of wall that the beam sustains will be of 
 
66 WBOUGHT IRON AND STEEL. 
 
 a triangular shape, the height being one-fourth of the span. 
 Owing to frequent irregularities in the bonding, it is best to con= 
 sider the height as one-third of the span. 
 
 The weight of brick work for each inch of thickness, is about 
 10 Ibs. per square foot. Therefore the weight of the triangular 
 mass of brick that the beam supports is found as follows : 
 
 span, 
 
 x o~~ in feet 
 x 10 times the thickness of the wall in inches 
 
 = weight in Ibs. ; or reducing above to its more concise form, 
 
 W = Weight in Ibs. supported by the beam. 
 t Thickness of wall in inches. 
 s Span of beam in feet. 
 
 The greatest bending stress at the center of the beam, result- 
 ing from a brick wall of above shape, is the same as that caused 
 by a load one-sixth less concentrated at the center of the beam. 
 
 Example. What beam will be required to span an opening of 
 16 feet, and carry a solid brick wall 8 inches thick, the beam not 
 to be strained more than one-third of its ultimate strength ? 
 
 Weight of wall by the rule. W = 1( * ^ 256 rr 3,4 1 3 Ibs. 
 
 Considering the load as in middle of beam, it would be five- 
 sixths of above = 2,845 Ibs., or 5,690 Ibs. if evenly distributed. 
 
 By our table page 43, a 7" I beam 52 Ibs. per yard, comes near- 
 est to what is required, its greatest safe distributed load being 
 3.5 tons. The deflection under this load will be about .45 of an 
 inch, found as described on page 89. 
 
 If a wall has openings such as windows, etc.. the imposed 
 weight on the beam may be greater "than if the wall is solid. 
 
 For such a case consider the outline of the brick, which the 
 beam sustains, to pass from the points of support diagonally to 
 the outside corners of the nearest openings, then vertically up 
 the outer line of the jambs, and so on if other openings occur 
 above. If there should be no other openings, consider the line 
 of imposed brick work to extend diagonally up from each upper 
 corner of the jambs, the intersection forming a triangle whose 
 height is one-third of its base, as described at beginning. 
 
FORMULAE FOB ROLLED IRON BEAMS. 67 
 
 APPROXIMATE FORMULA FOR ROLLED IRON 
 BEAMS. 
 
 The following rules for the strength and stiffness of rolled 
 iron beams of various sections are intended for convenient ap- 
 plication in cases where strict accuracy is not required. 
 
 The rules have been derived from the authoritative formula?. 
 Those for rectangular and circular sections are correct, while 
 those for the flanged sections are limited in their application to 
 the standard shapes as given in our tables. They will be found 
 to give results which have been proved by experiment to be suf- 
 ficiently accurate for practical purposes. When the section of 
 any beam is increased above the standard minimum dimensions, 
 the flanges remaining unaltered, and the web alone being thick- 
 ened, the tendency will be for the ultimate load as found by the 
 rules to be in excess of the actual, but within the limits that it 
 is possible to vary any section in the rolling, the rules will apply 
 without any serious inaccuracy. 
 
 IN THE TABLES OF FORMULAE 
 
 Column I. indicates the cross section of the beam. 
 
 Column II. gives the ultimate load applied at the center of a 
 beam supported at each end. 
 
 Column III. gives the ultimate load uniformly distributed over a 
 beam supported at each end. 
 
 Column IV. indicates the deflection under any load, w (not ex- 
 ceeding one-half the ultimate load) at the middle 
 of the beam. 
 
 Column V. gives the deflection for a load uniformly distributed. 
 
 SAFE LOADS. 
 
 The ultimate load given in the tables is defined on page 32. 
 One- third of this should be accepted as the greatest safe station- 
 ary load, and from one-fourth to one-sixth of the same when a 
 moving or fluctuating load is imposed, according to the way it is 
 applied, cr the degree of stiffness required. See table, page 34. 
 
 10 A = WEIGHT PER YARD IN LBS. 
 
 The area, A, of any cross section of wrought iron may be ob- 
 tained by dividing its weight per yard by 10 ; and vice versa, its 
 weight per yard may be found by multiplying its area in square 
 inches by 10 ; e.g. the area of a beam weighing 50 Ibs. per yard 
 is five square inches. 
 
68 
 
 WEOUGHT IBON AND STEEL. 
 
 * 
 
 a 
 
 ?.! 
 
FORMULA FOB WROUGHT IRON BEAMS. 
 
 9 
 
 s 
 
 ^ 
 
 
 SJ 
 
 
 ^ 
 
 -^ 
 
 Q 
 
 ^ 
 
 
 00 
 
 o* 
 
 CD "^ 
 
 (^ o 
 
 H 
 
 1-1 OJ 
 
 W CO 
 
 w "^ 
 
 CO ^ 
 
 
 fc 
 
 I 
 
 
 5t= 
 
 i 
 
 |\ _ /I 
 
 IT "\| 
 
70 "WROUGHT IEON AND STEEL. 
 
 EXAMPLES CALCULATED FROM PRECEDING TABLES. 
 SOLID RECTANGULAR SECTIONS. 
 
 Example 1. To find the breaking load for any solid rectan- 
 gular beam loaded in the middle. 
 
 ~r C = Solid rectangular bar, 2 inches wide, 4 inches 
 j* deep and 10 feet between supports. Then, from For- 
 
 1 mula No. 1 , we have * x 4.16 tons breaking 
 
 lv 
 
 load in middle of beam. 
 
 Example 2. To find the uniformly-distributed breaking load 
 for same beam. 
 
 Formula No. 2. ?' 6 x 8 = 8.32 tons breaking load uni- 
 formly distributed. 
 
 Example 3. To find the deflections for above beam under the 
 greatest safe loads ; viz., one-third breaking loads. 
 
 Formula No. 3. *' 39 * =0.36 inches, for a load of 1.39 
 
 oO x 8 x lo 
 
 tons in middle. 
 
 Formula No. 4. - 77 x 10 ? = 0.45 inches, for a load of 2.77 
 48 x 8 x 16 
 
 tons distributed. 
 
 HOLLOW RECTANGULAR SECTIONS. 
 
 Example 4. To find the breaking loads for any hollow rec- 
 tangular beam supported at both ends. 
 
 Let be a hollow rectangular section, 4 inches wide, 
 "t 8 inches deep, external dimensions ; 3 inches wide, 6 
 inches deep, internal dimensions; 15 feet between sup- 
 ports. 
 
 Formula No. 5. _K*JL9- < 18 * 6 U = 13.83tons,bre a k- 
 15 
 
 ing load in middle ; and multiplying this result by 2, we have 
 25.66 tons for the breaking load uniformly distributed. 
 
EXAMPLES FROM PRECEDING TABLES. 71 
 
 Example 5. To find the deflection of this beam with three tons 
 in middle ; also with six tons distributed. 
 
 flection with three tons in middle. 
 Formula No. 8. J-.., inehes de . 
 
 flection with six tons distributed. 
 
 SOLID AND HOLLOW CYLINDERS. 
 
 The preceding examples for rectangles will 
 apply to the circular sections by merely sub- 
 stituting the proper co-efficients as given in 
 Formulae 9 to 16 inclusive. 
 
 EVEN-LEGGED ANGLES AND TEES. 
 
 Example 6. To find the breaking loads for an even-legged 
 angle or tee, used as a beam supported at both ends. 
 
 Weight, 37 Ibs. per yard or 3.7 square 
 't, inches section; 12 ft. between supports. 
 
 Formula No. 18. 2 ' S * 
 
 tons breaking load uniformly distributed, or 1.73 tons breaking 
 load in the middle. 
 
 Example 7. To find the deflection of the above beam under 
 a load suspended from the middle of the beam. 
 Load = 1500 Ibs. = . 75 tons. 
 
 Formula No. 19. ' 6 = - 64 inches deflection - 
 
 Theoretically an angle has the same transverse strength as a 
 tee of the same dimensions. But owing to the difficulty of dis- 
 posing the load as symmetrically on the angle as on the tee, the 
 latter shape generally yields better results by experiment. 
 
72 WROUGHT IRON AND STEEL. 
 
 CHANNEL BARS. 
 
 Example 8. To find the breaking loads for a channel bar 
 used as a beam supported at both ends. 
 
 Channel bar 9 inches deep, 70 pounds per yard ; 7 square 
 inches section, 14 feet between supports. 
 
 Formula No. 22. --*^ - = 17.1 tons distributed 
 
 breaking load, or half this weight will be the breaking load in 
 the middle. 
 
 Example 9. To find the deflection of above beam under 
 greatest safe distributed load. 
 17.1 
 
 3 
 
 = 5.7 tons greatest safe distributed load. 
 
 Formula No. 24. j>.7 x 2744 _ g g ^ deflection. 
 80 x 7 x 81 
 
 I BEAMS. 
 
 Example 10. To find the breaking loads for an I 'beam, 
 loaded in the middle and supported at both ends. 
 
 A 15" I beam, 200 Ibs. per yard, 20 square inches area, 
 
 20 feet between supports. Formula No. 29. 2-1 x 20 - 
 
 = 31 . 5 tons middle breaking load ; one-third of which 
 (10.5 tons) will be greatest safe load in middle, or twice 
 this (21 tons) equals greatest safe load distributed. 
 
 Example 11. To find the deflections for the same I beam 
 under the above greatest safe loads. 
 
 Formula No. 31. = .33 inches under a load of 
 
 56 x 20 x 225 
 
 10.5 tons in the middle. 
 
 Formula No. 32. 21 * 800( L, g = .41 inches under a load of 
 90 x 20 x 225 
 
 21 tons uniformly distributed. 
 
 Although the preceding rules for I beams and channels give 
 results which are substantially correct for all the standard sec- 
 
EXAMPLES FROM PRECEDING TABLES. 73 
 
 tions as ordinarily rolled, yet they are not strictly accurate, and 
 not applicable to the heavier-built beams, whose flanges are 
 much larger, relatively to the web, than is the case in the aver- 
 age rolled beams. For such cases, the following formula is 
 
 , Q.QA'D' + l.2a'd f , , . , , . 
 correct. = breaking load in middle of beam. 
 
 A' = Area of one flange. 
 
 D = Depth between centres of flanges. 
 
 a = Area of web. 
 
 d = Depth of web. 
 
 For example, a beam 20 inches deep, flanges 8" x 1", web " 
 - , thick, 20 feet between supports, 
 
 6.6 x 8 x 19" + 1.2 x 4.5 x 18 
 
 55 tons 
 20 
 
 breaking load in middle of beam ; whereas the Rule in 
 Table for Rolled Beams would give a similarly placed load of 
 2.1 x 20.5 x 20 
 
 20 
 
 = 43 tons. 
 
 When the load is concentrated away from the centre of beam, 
 the ultimate load will be to the load at centre as the square of 
 half the span is to the product of the segments formed by posi- 
 tion of load. 
 
 Example. A beam 20 feet between supports has its load 
 placed 5 and 15 feet respectively from each end : the breaking 
 load at that point is to the calculated breaking centre load as 100 
 is to 75. 
 
 BEAMS HAVING NO LATERAL SUPPORT BETWEEN 
 BEARINGS. 
 
 If beams are us?d without any support sideways, the ten- 
 dency to fail, by lateral bending of the top flange, will increase 
 with the length of the beam ; and, in such cases, it is better to 
 limit the application of the preceding rules to beams whose 
 lengths do not exceed 20 times the width of the flange, gradually 
 increasing the factor of safety for longer beams ; so that, when 
 
74 WROUGHT IRON AND STEEL. 
 
 the beam reaches a length equal to 70 times the width of the 
 flange, the greatest safe load would be about one-sixth of the 
 calculated breaking load, or the proper factor of safety for the 
 latter beam would be double that for the former. (See page 36.) 
 
 CANTILEVER BEAMS. 
 
 The application of the preceding rules to overhanging beams 
 fixed at one end and free at the other, is best indicated by sup- 
 posing a beam with both ends supported to be inverted, and the 
 reaction of the supports considered as the positive load. 
 
 w w 
 
 / 
 
 It is then evident that a beam, A C (see above illustration), 
 both ends supported, will be strained with a middle load, W, in 
 an equal manner to a cantilever, A B or B C, of half the length 
 of A G and having a similar section, and bearing one-half the 
 
 load(orf) 
 
 at its end. 
 
 EXAMPLES FOR CANTILEVER BEAMS. 
 
 A rectangular bar, 6" x 2", built into a wall and projecting 
 eight feet. For load concentrated at its end, take one- 
 fourth the co-efficient in Table for Beams with both ends 
 
 supported and load in middle. =2.9 tons 
 
 ultimate load. Deflection under one-third of above, or say nine- 
 tenths of a ton ; substituting one-sixteenth of the co-efficient for 
 
 9 x 512 
 deflection when load is in middle. ~ = 0.56 inches 
 
 deflection at end. 
 
 A 12-inch I beam, 15 square inches section, extends 
 10 feet beyond a rigid support. For a load evenly dis- 
 tributed, take one-fourth the co-efficient for a beam 
 supported at both ends, bearing a distributed load. 
 
 1.05 x 15 x 12 ->y * .1 u i i j j- x M j. i 
 -^ = 18 . 9 tons breaking load distributed. 
 
EXAMPLES FKOM PBECEDING TABLES. 75 
 
 For deflection under five tons distributed, substitute one-sixth 
 of the co-efficient for deflection in Rule for Beams supported at 
 
 both ends with load in* middle. -^ = 0.25 inches 
 
 deflection at end of beam. 
 
 CONTINUOUS BEAMS. 
 
 When a beam is continuous over several supports, or when 
 both ends are as rigidly secured as is necessary at the fixed ends 
 of a cantilever, the beam is practically in the same condition as 
 a non-continuous beam of shorter span. 
 
 When the load is applied at the middle of the span, the ulti- 
 mate breaking load of a continuous beam is equal to twice that 
 for a non-continuous beam similarly loaded and of the same 
 length and section. 
 
 When the load is evenly distributed, the ultimate load for a 
 continuous beam is 1.5 times greater than the ultimate load for 
 a non-continuous beam under the same conditions and of the 
 same length and section. 
 
 The deflection of a continuous beam is one-fourth that of a 
 non-continuous beam when similarly loaded. 
 
 To find the strength and stiffness of continuous beams, take 
 the rules given for non -continuous beams and alter the co-efficients 
 in the proportions stated. 
 
 EXAMPLES FOR CONTINUOUS BEAMS. 
 
 A 4-inch I beam of three square inches section is continuous 
 over supports twenty feet apart. To find the greatest safe load 
 uniformly distributed, and corresponding deflection, take 
 1.5 times the co-efficient for a similar non-continuous beam. 
 
 ^ = 3 . 78 tons breaking load, or 1 . 26 tons safe distrib- 
 uted load. For deflection, take four times the co-efficient for the 
 
 same class of non-continuous beam. ^ i ^ = 0.58 of an 
 
 360 x 3 x 16 
 
 inch deflection. 
 For a continuous beam bearing load in middle, take twice the 
 
76 
 
 WROUGHT IRON AND STEEL. 
 
 co-efficient given for the strength of a similarly loaded non-con- 
 tinuous beam, and, for deflection of the former, take four times 
 the co-efficient given for the % latter beam. 
 
 It will be observed that these rules apply only to the interme- 
 diate spans of continuous beams, as, owing to the failure of con- 
 tinuity at one end of each outer span, the conditions are altered. 
 If, however, the outer ends of a continuous beam overhang the 
 end-supports from one-fifth to one-fourth of a span, and bear the 
 same proportion of load as the parts between supports, then the 
 outer spans may be of same length as the intermediate spans, 
 subject to the same load, and the strength and stiffness are de- 
 termined by the same rules ; otherwise, the outer spans ought 
 to be only four-fifths of the length of the intermediate spans 
 when the load is distributed, or three-fourths of the same when 
 the load is concentrated in the middle ; or, if the lengths of 
 spans are all alike, the loads on outer spans ought to be reduced 
 in the same proportion. 
 
 The following table exhibits the relative proportions of 
 strength and stiffness existing between the various classes of 
 beams when they have the same lengths and uniform cross 
 sections ; the deflections being comparative figures for the same 
 loads. 
 
 KIND OF BEAM. 
 
 Breaking 
 loud as 
 
 Deflection 
 as 
 
 Fixed at one end loaded at the other 
 
 l 
 
 16 
 
 Fixed at one end load evenly distributed. . . 
 
 * 
 
 6 
 
 Supported at both ends load in middle 
 
 1 
 
 1 
 
 Supported at both ends load evenly distrib- 
 uted 
 
 2 
 
 | 
 
 Continuous beam load in middle 
 
 2 
 
 i 
 
 Continuous beam load evenly distributed. . . 
 
 3 
 
 R 
 ft 
 
 The breaking load and deflection of a beam supported at both 
 ends and loaded in the middle have been taken as the units in 
 
EXAMPLES FROM PRECEDING TABLES. 
 
 77 
 
 the preceding table, and the proportional strength and stiffness 
 of similar beams under different conditions given to find the 
 proper co-efficient for estimating the strength and stiffness of 
 the beam required, it is necessary to alter, in the given propor- 
 tions, the co-efficient for the same beam when supported at both 
 ends and loaded in the middle. 
 
 CHANGES OF CO-EFFICIENTS FOR SPECIAL FORMS OF 
 BEAMS. 
 
 For beams of the character denoted in list below, change the 
 co-efficients in table of formulae, pages 68-69, in the ratio given. 
 For concentrated loads and distributed loads respectively, 
 change the co-efficients given for the same kinds of loads in the 
 table. 
 
 KIND OF BEAM. 
 
 CO-EFFICIENT FOR 
 ULTIMATE LOAD. 
 
 CO-EFFICIENT FOB 
 DEFLECTION. 
 
 Fixed at one end, loaded at 
 the other. 
 
 One-fourth (\) of 
 the co-efficient of 
 table. 
 
 One - sixteenth 
 (A-) of the co- 
 efficient of ta- 
 ble. 
 
 Fixed at one end, load 
 evely distributed. 
 
 One-fourth (\) of 
 the co-efficient of 
 table. 
 
 Five - forty- 
 eighths (-&) of 
 the co-efficient 
 of tables. 
 
 Both ends rigidly fixed, or 
 a continuous beam, 
 with load in middle. 
 
 Twice the co-effi- 
 cient of table. 
 
 Four times the 
 co-efficient of 
 table. 
 
 Both ends' rigidly fixed, or 
 a continuous beam, with 
 load evenly distributed. 
 
 One and one-half 
 (1?) times the co- 
 efficient of table. 
 
 Four times the 
 co-efficient of 
 table. 
 
78 
 
 WKOUGHT IBON AND STEEL. 
 
 BENDING MOMENTS AND DEFLECTIONS FOR BEAMS 
 OF UNIFORM SECTION. 
 
 W= Total load. 
 
 L = Length of beam. 
 
 E = Modulus of elasticity. 
 / = Moment of inertia. 
 
 FORM OP BEAM AND POSITION OF 
 LOAD. 
 
 Maximum 
 bending 
 moment. 
 
 Maximum 
 shearing 
 stress. 
 
 Deflection. 
 
 Beam fixed at one end loaded at the 
 other : 
 
 
 
 
 + r\ F|G - 1 
 
 
 
 
 ^ 
 
 ^^N. 
 
 at point of 
 support 
 
 at point of 
 support 
 
 at end of 
 beam 
 
 i 
 
 (w) 
 
 ~ 37" 
 
 Draw triangle having A = WL. 
 Vertical lines give bending moments 
 at corresponding points on the beam. 
 
 
 
 
 Beam fixed at one end, load uni- 
 formly distributed : 
 
 7 N. 
 
 
 
 
 | ! 
 
 G. 2 
 
 at point of 
 support 
 
 2 ' 
 
 at point of 
 support 
 
 at end of 
 beam 
 _ WL* 
 
 ^ L o o o o o_o 
 
 Draw pnrabola having A = k 
 
 
 
 
 Ordinates give bending moments at 
 corresponding points on the benm. 
 
 
 
 
 Beam supported 
 ed in the middle : 
 
 at both ends, load- 
 
 
 
 
 ,/j 
 
 v FIG. 3 
 
 
 
 
 
 > IV 
 
 1 T\ 
 
 at middle 
 of beam 
 _ WL 
 
 4 ' 
 
 at point of 
 support 
 
 = "2" 
 
 at middle 
 of beam 
 '._ WL* 
 
 <_ L (g) - 
 
 Draw triangle having A = 
 
 Vertical lines give bending moments 
 at corresponding points on the beam. 
 
 
 
 
BENDING MOMENTS AND DEFLECTIONS. 
 
 79 
 
 BENDING MOMENTS AND DEFLECTIONS FOR BEAMS 
 OF UNIFORM SECTION. 
 
 W= Total load. 
 
 L = Length of beam. 
 
 E = Modulus of elasticity. 
 / = Moment of inertia. 
 
 FORM OP BEAM AND POSITION OP 
 LOAD. 
 
 Maximum 
 bending 
 moment. 
 
 Maximum 
 shearing 
 
 stress. 
 
 Deflection 
 
 Beam supported at both ends, load 
 
 
 
 
 uniformly distributed : 
 
 
 
 
 x^T^x' 4 
 
 at middle 
 
 at point of 
 
 at middle 
 
 / ^ ' ^\v 
 
 of he-am 
 
 support 
 
 of beam 
 
 A i\ 
 
 WL 
 
 W 
 
 WL 3 
 
 / 1 ! ! \ 
 
 8 ' 
 
 ~ 2' 
 
 ~ 76.8.E7' 
 
 WL 
 
 
 
 
 Draw parabola having A = 
 
 o 
 
 
 
 
 Ordinates eive bending moments at 
 corresponding points on the beam. 
 
 
 
 
 Beam supported at both ends, load 
 concentrated at any point : 
 
 
 at point of 
 
 
 
 
 support 
 
 
 
 
 next to a 
 
 
 / \v. FIG> 5 
 
 
 _ Wb 
 
 
 
 at position 
 of load 
 
 L ' 
 
 at position 
 of load 
 
 A ' ^^\^ 
 
 Wab 
 
 at point of 
 
 a 2 6 2 W 
 
 S\ j ! ' !\^ 
 
 L 
 
 support 
 
 ~ 3EIL' 
 
 ;:::: 1 ~ " -H 
 
 
 _ Wa 
 
 
 Wab 
 
 
 
 
 Draw triangle having A = . 
 L 
 
 
 
 
 Vertical lines give bending moments 
 at corresponding points on the beam. 
 
 
 
 
80 
 
 WKOUGHT IRON AND STEEL. 
 
 BENDING MOMENTS AND DEFLECTIONS FOR BEAMS 
 OF UNIFORM SECTION. 
 
 W = Total load. 
 
 L = Length of beam. 
 
 E = Modulus of elasticity. 
 / = Moment of inertia. 
 
 Beam supported at both ends, with concentrated load at various points : 
 R FIG. 6 
 
 Draw (by 5) the triangles having vertices at C, D and E, the verticals rep- 
 resenting bending moments for loads w 1 , w* and w 3 , respectively. Extend 
 FC to P, GD to R, and HE to S, making each long vertical equal to the sum 
 of the bending moments corresponding to its position. That is, FP = FO 
 + FI+ FJ. GR = GD + GL + GK. And HS = HE+ HN+ HM. Verti- 
 cals drawn from any point on the polygon, APBSB to AB, will represent the 
 bending moments at the corresponding points on the beam. 
 
 Beam rigidly secured at each end, and loaded in the middle. Or the inter- 
 mediate spans of a continuous beam, equally loaded in the middle of each 
 span : 
 
 A 
 
 FIG. 7 
 
 <- L 
 
 Points of contraflexure at #, ce, where Moment = 0. Distance of x from 
 either support = . Equal moments at middle and ends = . 
 WL* 
 
 WL 
 
 Deflection 
 
 j-' and at ends draw verticals BB', each 
 
 Draw a triangle having A 
 
 = ^p' join BB'. The vertical distances between BB' and the sides of the 
 triangle, represent the moments for corresponding points en the beam. 
 
BENDING MOMENTS AND DEFLECTIONS. 
 
 81 
 
 BENDING MOMENTS AND DEFLECTIONS FOR BEAMS 
 OF UNIFORM SECTIONS. 
 
 W = Total load. 
 
 L = Length of beam. 
 
 E = Modulus of elasticity. 
 / = Moment of inertia. 
 
 Beam rigidly secured at each end with load uniformly distributed. 
 Or the intermediate spans of a continuous beam bearing a uniformly dis- 
 tributed load on each span : 
 
 FIG. 8 
 
 Points of contraflexure x, x, where moment = 0. Distance of x from 
 either support = .21 L. 
 
 Draw parabola having A = -5 Draw verticals B, E', each equal to 
 
 O 
 TTTr 
 
 -p join BE', The vertical distances between BE' and the curve of the pa- 
 rabola represent the moments for corresponding points on the beam. 
 
 WL 
 
 Maximum moment at points of support = -r~-. 
 
 Moment at middle of beam = 
 
 WL 
 
 Maximum deflection at middle of beam 
 
 WL* 
 307. 27* 
 
82 WROUGHT IRON AND STEEL. 
 
 BEAMS FOR SUPPORTING IRREGULAR LOADS. 
 
 When a beam has its load unequally distributed over it, the 
 proper size of the beam can be determined by finding the maxi- 
 mum bending moment and proportioning the beam accordingly. 
 Equilibrium is obtained when the bending moment is equal to 
 the moment of resistance. That is, when the external force mul- 
 tiplied by the leverage with which it acts is equal to the strength 
 of the material in the cross section of the beam multiplied by 
 the leverage with which it acts. The ultimate moment of resist- 
 ance for a wrought-iron beam of symmetrical form is 
 
 42000 / 84000_/ 
 - depth d 
 
 d = depth of beam in the direction in which the force acts. 
 1= the moment of inertia about the axis at right angles to the 
 
 direction of the force. 
 
 The greatest sai'e moment of resistance as adopted in our tables 
 is one-third (j) of above, 
 
 ^_ 280007 M I 
 
 ~ ' 
 
 38000"^ 
 
 The co-efficient to be changed according to the factor of safety 
 
 desired. The rule would thus be ' - = - 
 
 Co-efficient d 
 
 RULE FOR BEAMS BEARING IRREGULAR LOADS. 
 
 Find by the methods described in preceding article the maxi- 
 mum bending moment in inch-lbs. for the loads. Divide the 
 moment by the proper co-efficient as described above. Find in 
 the tables, pages 92-96, a beam whose inertia divided by its 
 depth is not less than this quotient; which will be the beam re- 
 quired. 
 
 In some instances the maximum bending moment can be most 
 readily found by the use of diagrams, as described in the succeed- 
 ing article. 
 
 When this is done use any convenient scale, making all loads 
 
RULES FOB BEAMS BEARING IRREGULAR LOADS. 83 
 
 and all distances respectively of the same denominations. The 
 maximum bending moment can then be measured to scale. 
 
 Example. An I beam 8 feet long is to be fixed at one end and 
 loaded at the other with 5,000 Ibs. and carrying also an evenly 
 distributed load of 8,000 Ibs. What size of beam should be used 
 so as not to ba strained over one-third of its ultimate capacity ? 
 
 Moment for end load = 5,000 x 96 = 480,000 inch-lbs. 
 
 " distributed load = 8>00 ' x 96 = 384,000 " 
 
 A __ 
 
 Total = 864,000 " 
 For one-third of ultimate the co-efficient will be 
 
 28,000. 
 
 864.000 J 
 
 28,000 - ~d 
 
 By Column VII., page 92, for a 12" 168 Ib. I beam, J = 
 371.98, which divided by 12 = 30.99; or a 15" 145 Ib. I beam, 
 
 -5- =34.7. The latter beam would be stronger and lighter. 
 
 In the following example the maximum bending moment can 
 be very readily obtained by a diagram as described in Fig. 6 of 
 the preceding article. 
 
 Example. A beam 20 feet long between supports, will carry 
 three loads, which we will call A, B, and C. 
 
 A 4,000 Ibs. and is 4 feet from one end of the beam. 
 C 6,000 Ibs. and is 3 feet from the other end of the beam. 
 B = 5,000 Ibs. and is 5 feet from C and 8 feet from A. 
 
 What beam is best to use for above, not strained over one- 
 fourth of the ultimate ? Describe the diagram as per Fig. 6, 
 when the following bending moments in ft. -Ibs. will be ob- 
 tained. 
 
WROUGHT IRON AND STEEL. 
 
 At point A 
 
 For load 4.. 12,800 
 B.. 8,000 
 C.: 3,600 
 
 At point B 
 
 For load B.. 24,000 
 A.. 10,800 
 C. . 6,400 
 
 At point C 
 
 For load C. . 15,300 
 B.. 8,900 
 A.. 2,400 
 
 Total 24,400 
 
 Total.... 41,200 
 
 Total. . . . 26,600 
 
 The maximum moment at B = 41,200 ft.-lbs. or 494,400 inch. 
 Ibs. For one-fourth of ultimate strength co-efficient = 21,000. 
 
 494.400 
 21,000 
 
 = 23.5 = V 
 
 By table on page 92, for a 12" 120 Ib. I beam L = 22.74, be- 
 
 d 
 
 ing slightly deficient. A 12" 125 Ib. I beam will be ample. 
 
 If more lateral stiffness is required than a single beam affords, 
 use a pair of channels separated and braced horizontally. Two 
 
 12" 75 Ib. channels -j = 23.6, would suit above purposes. 
 
 NOTE. The tables of elements, except where otherwise speci- 
 fied, are calculated for dimensions in inches and weights in Ibs., 
 consequently in examples of above character it is necessary to 
 obtain bending moments in inch-lbs. 
 
 BEAMS SUBJECT TO BOTH BENDING AND COM- 
 PRESSION. 
 
 When a beam is subjected to bending action and simulta- 
 neously has to act as a strut by resisting compression, the stress 
 of the fibres of the beam in tension will be relieved and those in 
 compression correspondingly augmented. 
 
 No general rules can be given for such conditions, as every 
 particular case requires its own proper determination. The fol- 
 lowing methods, though not strictly correct, will give safe re- 
 sults for some simple forms of trussed girders, etc. 
 
 (1.) When the beam is subject to compression but is so con- 
 fined laterally that it cannot fail by bending like a strut. 
 
BEAMS SUBJECT TO BENDING AND COMPRESSION. 85 
 
 Rule. Find the section of beam required to resist bending, 
 then allowing from 10,000 to 15,000 Ibs. per square inch of sec- 
 tion for the compression, according to the factor of safety used, 
 add the area so found to the first area, which will give the sec- 
 tion of required beam. 
 
 Example. What I beam is required to span an opening of 30 
 feet, to be trussed 3 feet deep between centres in the manner 
 illustrated in Fig. 6, page 165? (this trussed beam carries a brick 
 wall which weighs 500 Ibs. per lineal foot, but which braces the 
 beam from yielding sideways), the beam to be proportioned for 
 a safety factor of four ? 
 
 Here the beam can be considered as composed of two separate 
 beams, reaching from the centre to each end, each being 15 feet 
 long, carrying a distributed load of 15 x 500 = 7,500 Ibs., and 
 subject to a compression resulting from the trussing of 18,750 
 Ibs. Our approximate tables for beams, on page 69, will be 
 found most convenient for such calculations as the above, and 
 are sufficiently accurate for practical purposes. For I beam, 
 
 dividing co-efficient by 4 we have ' = safe distributed 
 
 load = 3. 75 tons. 
 
 By trial we find for an 8" 65 Ib. I beam ltQ *' 5 *- = 3.64, 
 
 10 
 
 or nearly correct. 
 
 For the compression, allowing 12,500 Ibs. per square inch, we 
 require l square inches. Therefore an 8" I beam, 8 square 
 inches section, will be safe. 
 
 If desirable to use a deeper, lighter beam, try a 9-inch beam 75 
 Ibs. per yard ; allowing 1| square inches for the compression, we 
 
 have a section of 6 square inches remaining ; = 3.78. 
 
 15 
 
 The latter beam being both stronger and lighter than the 8- 
 inch. 
 
 (2.) When the beam is subject to compression and is liable to 
 fail like a horizontal strut by lateral flexure. 
 
 Rule. Consider first the resistance as a strut and then make 
 the necessary increment of section to resist the bending stress, 
 remembering that if the addition is made to the flanges then 
 only flange stresses have to be considered, but if the increased 
 
86 WROUGHT IRON AND STEEL. 
 
 area is obtained by thickening the web of I beam or channel sec- 
 tions, then the additional area so obtained should be treated as a 
 rectangular section whose thickness is the amount added to the 
 web, and whose depth is the depth of the beam. 
 
 Example. A. trussed girder of the form exhibited in Fig. 8, 
 page 165, is a box section made up of two channels separated with 
 flanges outward, and plated top and bottom. The whole girder 
 is 30 feet long and is loaded 1,000 Ibs. per lineal foot. The com- 
 pression resulting from the trussing is 25,000 Ibs. The structure 
 has no lateral bracing. What will be safe proportions for it, the 
 stresses not to exceed of the ultimate ? 
 
 It is evident that we have to consider it as a flat-ended strut 
 30 feet long liable to fail horizontally, and also as a series of 3 
 beams each 10 feet long and loaded with 10,000 Ibs. evenly dis- 
 tributed. Trying 2 lightest 5" channels, each 2.27 square inches 
 section, separated 5" so as to be covered by 9" plates, we have 
 (omitting the plates in this calculation,) the radius of gyration 
 around vertical axis (see page 110) =.3.25 inch- 
 
 l 
 es, - = 110, one-fifth of ultimate (by Table I, 
 
 page 118) - 5,600 Ibs. per square inch, or 5,600 
 x 4i = 25,200 Ibs. safe resistance, which is 
 ample. Now proportioning the plates to resist 
 the bending strain we have maximum bend- 
 
 1 9ft v 1 000 
 
 ing moments (see page 78), ~ -' = 150,000 inch-lbs. 
 
 o 
 
 The plates act with a leverage equal to the depth of the chan- 
 nel, viz., 5"; '- = 30,000 Ibs. tension on top or compres- 
 5 
 
 sion on bottom plate, which, allowing for 10,000 Ibs. per square 
 inch, and allowing for loss by rivets, will require a plate f" 
 thick. 
 
 (3 ) Taking the last example, if it was desired to form the sec- 
 tion out of a pair of channels latticed top and bottom with no 
 cover plates, we would have to consider the section added to the 
 channels (being on the web alone), as a simple rectangular sec- 
 tion. By the formula on page 69, approximate rules, we find 
 that such a section only 5" deep would require a thickness of 
 3.8 inches, which is impracticable ; we have therefore to use deep- 
 
ELEMENTS OF PENCOYD STRUCTURAL SHAPES. 87 
 
 er and heavier channels. Trying 8" channels separated as be- 
 fore 5 inches, with flanges outward, and having radius of gyra- 
 
 tion for the pair around vertical axis = 3.4, = 106. Safe load 
 
 90 nftft 
 
 ^ J> 1W = 5,800 Ibs. per square inch. As the compression is 25,OCO 
 5 
 
 Ibs., there is required 4.8 square inches for this purpose. By 
 
 formula 2, page 68, - 52 x ^ ea x 8 _ 5 tons, from which is 
 
 found the area required to resist bending 12 square inches. 
 12 4- 4.3 = 10.3 square inches for 2 channels, or the heaviest 8 
 channels 80 Ibs. per yard would be required. 
 
 By the same method we find 10" channels 68 Ibs. per yard, 
 will answer the purpose, or our lightest 12" channels 60 Ibs. 
 per yard, will exactly meet the requirements and be the lightest 
 channel that can be used in the manner proposed for the pur- 
 pose. 
 
 In cases where the load is concentrated at the truss points, 
 there being no bending stress, the resistance as a strut has only 
 to be considered, and when braced laterally the strut length is 
 reduced to the distances between bracir.g. 
 
 ELEMENTS OF PENCOYD STRUCTURAL SHAPES. 
 
 In the following tables, pages 88, 91, various properties of 
 rolled structural iron are given, whereby the strength or stiff- 
 ness of any shape can be readily determined. 
 
 SYMBOLS. 
 
 I = Moment of inertia. 
 E Modulus of elasticity. 
 W = Load on beam in net tons. 
 w = Load on beam in pounds, 
 R = Radius of gyration. 
 A Total area of cross section. 
 L Length between supports in feet. 
 
 I = Length between supports in inches. 
 
88 WROUGHT IRON AND STEEL. 
 
 Column I. Chart number. 
 
 Columns III. to VI. Details of the sectional areas in square 
 inches. The flanges being taken the entire width 
 of section, and the web considered between the 
 flanges. 
 
 Columns VII. and VIII. The moments of inertia, respectively, 
 at right angles to and parallel with web of beam. 
 In all cases the axes referred to pass through the 
 centre of gravity of the cross-section, as illustra- 
 ted at the head of each table. 
 
 Columns IX. and X. The' radii of gyration in inches A/ . 
 
 r A 
 
 When R 2 is required, simply divide the moment 
 of inertia by the area of the section. The values 
 of / and R have all been carefully calculated by 
 the formulae given on pages 102-111. The tables 
 give the value of 1 for the minimum section 
 of each particular shape, but the section can 
 be increased in area up to the maximum limit 
 given in the descriptive tables, pages 2-12, 
 and the value of / can be readily obtained 
 for any enlarged section as described on pages 
 106-108. 
 
 Column XI. Co-efficient for the greatest safe load evenly dis- 
 tributed over the beam. This is the calculated 
 load in net tons for a beam of the given size and 
 section, one foot long, and is derived from the 
 
 formula -- = -, which gives re- 
 
 8 depth of beam 
 
 suits averaging one-third of the ultimate strength 
 of the beam. The safe distributed load for any 
 beam of the size and section given in Columns II. 
 to VI. can be found by dividing the correspond- 
 ing co-efficient in column XI. by the length of 
 the beam between supports, in feet. 
 
 Example. The greatest safe load that can be evenly distrib- 
 uted on a beam 10 inches deep having a sectional area of 9.04 
 
 "1 Qft A. 
 
 square inches and spanning 12 feet is 10 ' = 11.5 tons. 
 
ELEMENTS OF PENCOYD STRUCTURAL SHAPES. 89 
 
 If -the load is concentrated in the middle of the beam, one- 
 half this result, or 5.75 tons, is the greatest safe load. 
 
 If the sectional area of the beam is increased, find the moment 
 of inertia for the increased section as described on page 106, and 
 
 the co-efficient for a distributed safe load = - - -3- _ . 
 
 depth of beam 
 
 Example. The 10" beam taken in last example, 9.04 square 
 inches area, is increased to 10.6 square inches section. The in- 
 ertia of enlarged section is found as per formula on page 106, 
 1.56 = (increase of area) x 100 = (square of depth) 10 
 
 - - - ~j - = - = - - = lo. + 1 4o . o 
 
 I/O 
 
 (inertia, col. vii., page 92,) 161 .3 or moment of inertia desired. 
 Co-efficient for safe load = 161> ^ > -^ = 150.5. Dividing this 
 
 co-efficient by the span in feet (12), gives -^f~ = 12.54 tons as 
 
 \4i 
 
 the maximum safe load distributed, or 6.27 tons in the middle of 
 the beam. 
 
 Lateral Flexure. It will be noted that when subjected to such 
 loads as above obtained, the beams are presumed to be secured 
 from bending sideways, and it will be safest to limit the applica- 
 tion to beams secured laterally at intervals, in length not ex- 
 ceeding twenty times the width of flange. See preface to tables 
 of safe loads for beams, page 36. 
 
 Columns XII. and XIII. Deflections. 
 
 The figures in the tables are the calculated deflections for 
 beams of the sizes and sections given, one foot long between 
 bearings and supporting a load of one ton. They are derived by 
 
 means of the formulae X = deflection for load in middle of 
 
 beam. ^ = deflection for load evenly distributed. 
 
 7o . 
 
 The modulus of transverse elasticity is assumed as 26,000,000 
 Ibs. The elasticity of rolled iron is somewhat uncertain, it is 
 frequently quoted as high as 29,000,000 Ibs., and experiments 
 on bars of exceptionally stiff iron will often give results much in 
 excess of this. But recent experiments on rolled beams show 
 that 26,000,000 Ibs. is a fair average for this form of wrought 
 iron. See page 19. 
 
90 WROUGHT IRON AND STEEL. 
 
 The deflection of any beam of the sectional area given in cols. 
 IV. to VI., and loaded within the elastic limit, is found by mul- 
 tiplying the corresponding co-efficient in cols. XII., XIII., by 
 the weight in tons and the cube of the length in feet. 
 
 Example. A. 12" I beam, 11.95 square inches section, 13 feet 
 between supports, carries an evenly distributed load of 15 tons. 
 Deflection- .0000063 x 15 x 13 3 = .207 inches. 
 
 If the sectional area of this shape is increased, the value of 1 
 for the enlarged section must be found as described in previous 
 example. By reducing the formulae for deflection to their sim- 
 plest forms we obtain : 
 
 1 1 r T :< 
 
 = deflection in inches for load in middle. 
 
 3627 
 
 "WJ ' J 
 
 =-^4- = deflection in inches for distributed load. 
 5807 
 
 Example. The 12" beam in previous example 11.95 square 
 inches area, is increased to 13.8 square inches The inertia of 
 enlarged section is found as per formula, page 106. 
 1 . 85 (increase of area) x 144 (square of depth) _ 
 
 -i n ** * l~ * * ~" 
 
 inertia, col. vii., page 92, = 295.06, or moment of inertia desired. 
 
 For beams of the same depth, but of any sectional area, thts 
 deflection remains uniform so long as the loads bear a uniform 
 ratio to the strength of the beam. For this reason, the single 
 column of deflections applies to any section of the same size of 
 beam, in the tables of safe loads. 
 
 Column XIV. Maximum load in tons. 
 
 There is a limit in the length of beams at which the rule for 
 safe loading ceases to apply. This point is reached when the 
 load attains the safe limit of resistance offered by the web of the 
 beam against crippling. 
 
 The maximum load can be placed on any beam shorter than 
 the length indicated, but must not be exceeded. It is obtairied 
 by Gordon's formula, taking 6 tons per square inch as the safe 
 resistance of wrought iron to crushing. 
 
ELEMENTS OF PENCOYD STBUCTUBAL SHAPES. 91 
 
 W = 6^ d = depth of beam, 
 
 -j , P t thickness of web. 
 
 3000^ I = d x secant 45 (P = 2cf). 
 
 Example. An 8" 65 Ib. beam has a maximum load of 10.46 
 tons, which corresponds to the greatest safe load on a beam of 
 this section, 7.7 feet between supports, if the load is distributed, 
 or 3.85 feet if the load is at middle of beam. If this shape is in- 
 creased to 7-i square inches area, having a web -fc" thick, then 
 maximum safe load becomes 
 
 6 " x 8 " x -i 
 
92 WROUGHT IRON AND STEEL. 
 
 ELEMENTS OF FENCOYD BEAMS. 
 
 r 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 CHART 
 NUM- 
 BER. 
 
 1 
 
 SIZE 
 
 IN 
 
 INCHES. 
 
 WEIG'T 
 
 PER 
 
 YARD. 
 
 AREAS IN SQUARE INS. 
 
 MOMENT OP INERTIA. 
 
 Flanges 
 
 Web. 
 
 Total. 
 
 Axis A. B. 
 
 Axis C. D. 
 
 15 
 
 200 
 
 11.86 
 
 8.04 
 
 19.90 
 
 682.08 
 
 28.50 
 
 2 
 
 15 
 
 145 
 
 8.97 
 
 5.58 
 
 14.55 
 
 521.19 
 
 16.91 
 
 3 
 4 
 5 
 
 12 
 12 
 
 m 
 
 168 
 120 
 134 
 
 10.66 
 
 7.42 
 9.57 
 
 6.23 
 4.53 
 
 3.87 
 
 16.89 
 11.95 
 13 44 
 
 371.98 
 
 272.86 
 241.63 
 
 23.19 
 12.22 
 19.00 
 
 5* 
 
 104 
 
 108 
 
 7.33 
 
 3.50 
 
 10.83 
 
 195.42 
 
 12.45 
 
 6 
 
 10* 
 
 89 
 
 5.91 
 
 3.03 
 
 8.94 
 
 162.26 
 
 8.34 
 
 7 
 
 10 
 
 112 
 
 7.23 
 
 3.94 
 
 11.17 
 
 173.58 10.64 
 
 8 
 
 10 
 
 90 
 
 6.29 
 
 2.75 
 
 9.04 
 
 148.31 
 
 8.09 
 
 9 
 
 9 
 
 90 
 
 6.15 
 
 2.92 
 
 9.07 
 
 118.81 
 
 8.44 
 
 10 
 
 9 
 
 70 
 
 4.77 
 
 2.21 
 
 6.98 
 
 94.44 
 
 5.59 
 
 11 
 
 8 
 
 81 
 
 5.58 
 
 2.56 
 
 8.14 
 
 83.93 
 
 7.23 
 
 12 
 
 8 
 
 65 
 
 4.50 
 
 2.03 
 
 6.53 
 
 69.17 
 
 5.02 
 
 13 
 
 7 
 
 65 
 
 4.17 
 
 2.41 
 
 6.58 
 
 49.78 
 
 4.15 
 
 14 
 
 7 
 
 52 
 
 3.84 
 
 1.30 
 
 5.14 
 
 43.08 
 
 3.43 
 
 15 
 
 6 
 
 50 
 
 3 16 
 
 1.88 
 
 5.04 
 
 26.92 
 
 2.15 
 
 16 
 
 6 
 
 40 
 
 2.91 
 
 1.17 
 
 4.08 
 
 24.10 
 
 1.80 
 
 17 
 
 5 
 
 34 
 
 2.13 
 
 1.25 
 
 3.38 
 
 13.40 
 
 1.21 
 
 18 
 
 5 
 
 30 
 
 2.06 
 
 .88 
 
 2.94 
 
 12.50 
 
 1.09 
 
 19 
 
 4 
 
 28 
 
 2.15 
 
 .75 
 
 2.90 
 
 7.69 
 
 1.17 
 
 20 
 
 4 
 
 18.5 
 
 1.34 
 
 .56 
 
 1.90 
 
 5.14 
 
 .49 
 
 21 
 
 3 
 
 23 
 
 1.72 
 
 .53 
 
 2.25 
 
 3.29 
 
 .77 
 
 22 
 
 3 
 
 17 
 
 1.37 
 
 .34 
 
 1.71 
 
 2.66 
 
 .48 
 
ELEMENTS OF PENCOYD BEAMS. 
 
 93 
 
 ELEMENTS OF PENCOYD BEAMS. 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV- 
 
 li 
 
 
 SIZE IN INCHES. S 
 
 CHART 1 ,_ 
 
 -* NUMBER. 
 
 RADII OF GYRATION. 
 
 CO-EFFICIENT 
 SAFE LOAD 
 DISTRIBUTED. 
 
 CO-EFFICIENT FOR 
 DEFLECTION. 
 
 Axis A. B. 
 
 Axis C. D. 
 
 Load in 
 Centre. 
 
 Load Dis- 
 tributed. 
 
 5.86 
 
 1.20 
 
 424.41 
 
 . 0000041 
 
 .0000025 
 
 43.20 
 
 15 
 
 5.98 
 
 1.08 
 
 324.30 
 
 .0000053 
 
 .0000033 
 
 22.10 
 
 15 
 
 2 
 
 4.69 
 
 1.17 
 
 289.32 
 
 .0000074 
 
 .0000046 
 
 38.63 
 
 12 
 
 3 
 
 4.78 
 
 1.01 
 
 212.22 
 
 .0000101 
 
 .OCOOC63 
 
 22.22 
 
 12 
 
 4 
 
 4.24 1.19 
 
 214.78 
 
 .0000115 
 
 .0000072 
 
 22.13 
 
 101 
 
 5 
 
 4.25 
 
 1.07 
 
 173.71 
 
 .OOC0142 
 
 .0000089 
 
 17.71 
 
 101 
 
 6i 
 
 4.26 
 
 .97 
 
 144.23 
 
 .0000171 
 
 .0000107 
 
 13.35 
 
 104 
 
 6 
 
 3.94 
 
 .98 
 
 162.02 
 
 .0000159 
 
 .0000099 
 
 23.68 
 
 10 
 
 7 
 
 4.05 
 
 .95 
 
 138.43 
 
 .0000186 
 
 .0000116 
 
 13.18 
 
 10 
 
 8 
 
 3.62 
 
 .96 
 
 123.21 
 
 .0000232 
 
 .0000145 
 
 16.53 
 
 9 
 
 9 
 
 3.68 
 
 .89 
 
 97.94 
 
 .0000292 
 
 .0000183 
 
 9.94 
 
 9 
 
 10 
 
 3.21 
 
 .94 
 
 97.92 
 
 .0000329 
 
 .0000205 
 
 15.49 
 
 8 
 
 11 
 
 3.25 
 
 .88 
 
 80.70 
 
 .0000099 
 
 .0000249 
 
 10.46 
 
 8 
 
 12 
 
 2.75 
 
 .79 
 
 66.38 
 
 .0000546 
 
 .0000341 
 
 15.69 
 
 7 
 
 13 
 
 2.89 
 
 .82 
 
 57.44 
 
 .0000640 
 
 .0000400 
 
 6.17 
 
 7 
 
 14 
 
 2.31 
 
 .65 
 
 41.87 
 
 .0001025 
 
 .0000641 
 
 12.77 
 
 6 
 
 15 
 
 2.43 
 
 .66 
 
 37.49 
 
 .0001144 
 
 .0000715 
 
 6.50 
 
 6 
 
 16 
 
 1.99 
 
 .60 
 
 25.01 
 
 .0002059 
 
 .OC01C87 
 
 8.01 
 
 5 
 
 17 
 
 2.06 
 
 .60 
 
 23.33 
 
 .0002206 
 
 .0001379 
 
 4.86 
 
 5 
 
 18 
 
 1.63 
 
 .63 
 
 17.94 
 
 .0003589 
 
 .0002243 
 
 5.12 
 
 4 
 
 19 
 
 1.65 
 
 .51 
 
 12.00 
 
 .C005366 
 
 .0003354 
 
 3.03 
 
 4 
 
 20 
 
 1.21 
 
 .59 
 
 10.24 
 
 .0008382 
 
 .0005-239 
 
 4.11 
 
 3 
 
 21 
 
 1.25 
 
 .53 
 
 8.28 
 
 .0010366 
 
 .0006479 
 
 2.34 
 
 3 
 
 22 
 
94: WROUGHT IKON AND STEEL. 
 
 ELEMENTS OF FENCOYD CHANNELS. 
 
 I. 
 
 CHART 
 
 NUM- 
 BER. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 SIZE 
 
 IN 
 
 INCHES. 
 
 WEIO'T 
 
 PER 
 
 YARD. 
 
 AREAS IN SQUARE INS. 
 
 MOMENTS OP INERTIA 
 
 Flanges 
 
 Web. 
 
 Total. 
 
 Axis A. B. 
 
 Axis C. D. 
 
 30 
 
 15 
 
 148 
 
 6.50 
 
 8.36 
 
 14.86 
 
 451.51 
 
 19.05 
 
 31 
 32 
 
 12 
 
 12 
 
 88.5 
 60 
 
 4.59 
 
 2.87 
 
 4.24 
 3.07 
 
 8.83 
 5.94 
 
 182.71 
 123.71 
 
 7.42 
 3.22 
 
 34 
 
 10 
 
 60 
 
 3 5(5 
 
 2.43 
 
 5.99 
 
 92.08 
 
 4.2D 
 
 35 
 
 10 
 
 49 
 
 2.67 
 
 2.22 
 
 4.89 
 
 73.91 
 
 2.33 
 
 36 
 
 9 
 
 54 
 
 2.97 
 
 2.43 
 
 5.40 
 
 64.34 
 
 2.47 
 
 37 
 
 9 
 
 37 
 
 1.81 
 
 1.91 
 
 3.72 
 
 43.65 
 
 1.31 
 
 38 
 
 8 
 
 43 
 
 2.28 
 
 1.97 
 
 4.25 
 
 40.00 
 
 2.17 
 
 39 
 
 8 
 
 30 
 
 1.34 
 
 1.62 
 
 2.96 
 
 28.23 
 
 1.06 
 
 40 
 
 7 
 
 41 
 
 2.30 
 
 1.80 
 
 4.10 
 
 29.51 
 
 1.71 
 
 41 
 
 7 
 
 26 
 
 1.38 
 
 1.26 
 
 2.64 
 
 18.46 
 
 .90 
 
 42 
 
 6 
 
 33 
 
 2.04 
 
 1.25 
 
 3.29 
 
 18.37 
 
 1.46 
 
 44 
 
 6 
 
 23 
 
 1.09 
 
 1.18 
 
 2.27 
 
 11.67 
 
 .59 
 
 45 
 
 5 
 
 27.3 
 
 1.69 
 
 1.04 
 
 2.73 
 
 10.29 
 
 .86 
 
 46 
 
 5 
 
 19 
 
 .91 
 
 .97 
 
 1.88 
 
 6.67 
 
 .37 
 
 47 
 
 4 
 
 21.5 
 
 1.34 
 
 .81 
 
 2.15 
 
 5.16 
 
 .54 
 
 48 
 
 4 
 
 17.5 
 
 1.02 
 
 .73 
 
 1.75 
 
 4.14 
 
 .41 
 
 49 
 
 3 
 
 15 
 
 .86 
 
 .66 
 
 1.52 
 
 2.03 
 
 .32 
 
 50 
 
 ft 
 
 11.3 
 
 .69 
 
 .44 
 
 1.13 
 
 .80 
 
 .21 
 
 51 
 
 2 
 
 8.75 
 
 .55 
 
 .33 
 
 .88 
 
 .48 
 
 .08 
 
ELEMENTS OF PENCOYD CHANNELS. 95 
 
 ELEMENTS OF PENCOYD CHANNELS. 
 
 IX. 
 
 x 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 XV. 
 
 II. 
 
 I. 
 
 RADII OF 
 GYRATION. 
 
 Ill 
 
 CO-EFFICIENTS FOR 
 DEFLECTION. 
 
 p 
 
 81? 
 
 o 
 M 
 
 "si 
 
 
 h 3 
 
 
 
 
 
 
 Axis Uxie 
 
 W fc H 
 
 6-" 1 2 
 
 Load in 
 
 Load dis- 
 
 
 ||| 
 
 tt 
 
 og 
 
 A. B. 
 
 C. D. 
 
 o*P 
 
 centre. 
 
 tributed. 
 
 r 
 
 i 
 
 
 S 
 
 02 
 
 
 5.51 
 
 1.13 
 
 280.94 
 
 .0000061 
 
 .0000038 
 
 40.64 
 
 .95 
 
 15 
 
 30 
 
 4.55 
 
 .92 
 
 142.11 
 
 .0000151 
 
 .OOOC094 
 
 18.49 
 
 .71 
 
 12 
 
 31 
 
 4.56 
 
 .74 
 
 96.22 
 
 .0000223 
 
 .0000139 
 
 9.14 
 
 .62 
 
 12 
 
 32 
 
 3.92 
 
 .84 
 
 85.94 
 
 .0000298 
 
 .0000186 
 
 9.10 
 
 .75 1 
 
 10 
 
 34 
 
 3.89 
 
 .61) 
 
 68.98 
 
 .0000374 
 
 .0000234 
 
 7.25 
 
 .64 
 
 10 
 
 35 
 
 3.45 
 
 .68 
 
 66.73 
 
 .0000429 
 
 .0000268 ! 
 
 10.87 
 
 .67! 
 
 9 
 
 36 
 
 3.43 
 
 .59 
 
 45.27 
 
 .0000632 
 
 .0000395 
 
 6.38 
 
 .55 
 
 9 
 
 37 
 
 3.06 
 
 .71 
 
 46.66 
 
 .0000690 
 
 .0000431 
 
 8.77 
 
 .60 
 
 8 
 
 38 
 
 3.09 
 
 .60 
 
 32.94 
 
 .0000977 
 
 .0000611 
 
 4.79 
 
 .50 
 
 8 
 
 39 
 
 2.68 
 
 .65 
 
 39.35 
 
 .00009^5 
 
 .0000584 
 
 9.07 
 
 .65 
 
 7 
 
 40 
 
 2.64 
 
 .58 
 
 24.61 
 
 .0001495 
 
 .0000934 
 
 3.42 
 
 .48 
 
 7 
 
 41 
 
 2.36 
 
 .67 
 
 28.58 
 
 .0001501 
 
 .0000938 
 
 6.50 
 
 .66 
 
 6 
 
 42 
 
 
 
 
 
 1 
 
 
 
 
 
 2.27 
 
 .51 
 
 18.16 
 
 .0002363 
 
 .0001477 
 
 5.24 
 
 .46 
 
 6 
 
 44 
 
 1.93 
 
 .56 
 
 19.21 
 
 .0002680 
 
 .0001675 
 
 5.92 
 
 .61 
 
 5 
 
 45 
 
 1.88 
 
 .45 
 
 12.45 
 
 .0004136 
 
 .0002585 
 
 4.86 
 
 .42 
 
 5 
 
 46 
 
 1.55 
 
 .50 
 
 12.03 
 
 .0005349 
 
 .0003343 
 
 5.12 
 
 .53 
 
 4 
 
 47 
 
 1.54 
 
 .48 
 
 9.65 
 
 .0006667 
 
 .0004167 
 
 4.29 
 
 .45 
 
 4 
 
 48 
 
 1.16 
 
 .46 
 
 6.32 
 
 .0013584 
 
 .0008490 
 
 3.49 
 
 .51 
 
 3 
 
 49 
 
 .85 
 
 .43 
 
 3.33 
 
 .0034350 
 
 .0021470 
 
 3.20 
 
 .46 
 
 Si 
 
 50 
 
 .74 
 
 .3! 
 
 5 
 
 .0057230 
 
 .0035770 
 
 2.49 
 
 .37 
 
 2 
 
 51 
 
96 WROUGHT IRON AND STEEL. 
 
 ELEMENTS OP PENOOYD DECK BEAMS. 
 
 - c - 
 
 VJ ~ P 
 
 -- 
 
 J^-JB r 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 CHART 
 
 SIZE 
 
 WEIO'T 
 
 AREAS m SQUARE INS. 
 
 MOMENTS OF INERTIA 
 
 NUM- 
 
 IN 
 
 PER 
 
 1 
 
 
 BER. 
 
 INCHES. 
 
 YARD. 
 
 1 
 
 
 
 
 
 
 
 
 
 Fl'ge 
 
 1 
 
 Bulb. 
 
 Web. 
 
 Total. 
 
 Axis A. B. 
 
 Axis C. D. 
 
 60 
 
 12 
 
 104 
 
 3.59 
 
 2.89 
 
 3.90 
 
 10.38 
 
 221.98 
 
 9.33 
 
 61 
 
 11 
 
 91 
 
 3.26 
 
 2.52 
 
 3.28 
 
 9.06 
 
 164.09 
 
 7.64 
 
 62 
 
 10 
 
 80 
 
 2.87 
 
 2.19 
 
 2.96 
 
 8.02 
 
 118.22 
 
 6.13 
 
 63 
 
 9 
 
 72 
 
 2.50 
 
 2.06 
 
 2.61 
 
 7.17 
 
 84.77 
 
 4.92 
 
 64 
 
 8 
 
 61 
 
 2.17 
 
 1.85 
 
 2.09 
 
 6.11 
 
 57.66 
 
 3.63 
 
 65 
 
 7 
 
 52 
 
 1.86 
 
 1.55 
 
 1.80 
 
 5.2-1 
 
 34.40 
 
 2.59 
 
 66 
 
 6 
 
 42 
 
 1.52 
 
 1.28 
 
 1.38 
 
 4.18 
 
 21.95 
 
 1.64 
 
 67 
 
 5 
 
 34 
 
 1.22 
 
 1.04 
 
 1.11 
 
 3.37 
 
 12.04 
 
 .98 
 
ELEMENTS OF PENCOYD DECK BEAMS. 97 
 
 ELEMENTS OF FENCOYD DECK BEAMS. 
 
 =OP_ 
 
 IX. 
 
 RAD 
 GYRA 
 
 Axis 
 A. B. 
 
 X. 
 
 [I OF 
 TION. 
 
 Axis 
 C. D. 
 
 .95 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 XV. 
 
 SIZE IN INCHES. S 
 
 I. 
 
 CO-EFFICIENT 
 SAFE LOAD 
 DISTRIBUTED. 
 
 CO-EFFICIENTS FOB 
 DEFLECTION. 
 
 MAXIMUM LOAD 
 IN TONS. 
 
 DISTANCE, d, 
 FROM BASE TO 
 NEUTRAL Axis. 
 
 M 
 
 S| 
 
 60 
 
 Load in 
 centre. 
 
 Load dis- 
 tributed. 
 
 4.62 
 
 172.6 
 
 .0000122 
 
 .0000078 
 
 18.50 
 
 5.24 
 
 12 
 
 4.25 
 
 .92 
 
 139.5 
 
 .0000168 
 
 .0000105 
 
 15.72 
 
 4.68 
 
 11 
 
 61 
 
 3.84 
 
 .87 
 
 110.3! 
 
 .0000233 
 
 .0000146 
 
 15.26 
 
 4.27 
 
 10 
 
 62 
 
 3.44 
 
 .83 
 
 87.9 
 
 .0000325 
 
 .0000203 
 
 14.63 
 
 4.00 
 
 9 
 
 ! 
 63 
 
 3.07 
 
 .77 
 
 67.3 
 
 .0000478 
 
 .0000299 
 
 12.12 
 
 3.50 
 
 8 
 
 64 
 
 2.57 
 
 .71 
 
 45.8 
 
 .0000802 
 
 .0000501 
 
 11.30 
 
 3.20 
 
 7 
 
 65 
 
 2.29 
 
 .63 
 
 34.2 
 
 .0001257 
 
 .0000785 
 
 9.03 
 
 2.65 
 
 6 
 
 66 
 
 1.89 
 
 .54 
 
 22.4 
 
 .0002291 
 
 .0001432 
 
 8.01 
 
 2.22 
 
 5 
 
 67 
 
WROUGHT IRON AND STEEL. 
 
 ELEMENTS OF 
 
 PENOO YD ANGLES. 
 
 EVEN LEGS. 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 ~1~ 
 
 
 ca 
 
 
 
 MOMENTS OF 
 
 RADII OF 
 
 ss 
 
 1 
 
 
 S 
 
 INERTIA. 
 
 GYRATION. 
 
 g'i^ 
 
 1 
 
 SIZE IN INCHES. 
 
 || 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 ill 
 
 4 
 
 
 ^ 
 
 A. B. 
 
 C.D. 
 
 A. B. 
 
 C.D. 
 
 
 120 
 
 6 x 6 x f e 
 
 50.6 
 
 17.68 
 
 7.16 
 
 1.87 
 
 1.19 
 
 1.66 
 
 
 6x6x1 
 
 110.0 
 
 35.46 
 
 15.00 
 
 1.80 
 
 1.17 
 
 1.86 
 
 121 
 
 5 x 5 x -j 3 ^ 
 
 41.8 
 
 10.02 
 
 4.16 
 
 1.55 
 
 l.OOj 
 
 1.41 
 
 
 5x5x1 
 
 90.0 
 
 19.64 
 
 8.67 
 
 1.48 
 
 .98 
 
 1.61 
 
 122 
 
 4 x 4 x 3- 
 
 28.6 
 
 4.36 
 
 1.86 
 
 1.24 
 
 .81 
 
 1.14 
 
 
 4 x 4 x | 
 
 54.4 
 
 7.67 
 
 3.45 
 
 1.19 
 
 .80 
 
 1.27 
 
 123 
 
 3i x 3i x 
 
 24.8 
 
 2.87 
 
 1.20 
 
 1.07 
 
 .70 
 
 1.01 
 
 
 3| x 3* x fc 
 
 39.8 
 
 4.33 
 
 1.85 
 
 1.04 
 
 .69 
 
 1.10 
 
 124 
 
 3 x 3 x i 
 
 14.4 
 
 1.24 
 
 .51 
 
 .93 
 
 .60! 
 
 .84 
 
 
 3 x 3 x f 
 
 33.6 
 
 2.62 
 
 1.15 
 
 .88 
 
 .59 
 
 .98 
 
 125 
 
 2f x 2f x i 
 
 13.1 
 
 .95 
 
 .39 
 
 .85 
 
 
 .78 
 
 
 2| x 2| x i 
 
 25.0 
 
 1.67 
 
 .72 
 
 .82 
 
 !54 
 
 .87 
 
 126 
 
 2 x 24- x i 
 
 11.9 
 
 .70 
 
 .29 
 
 .77 
 
 .50 
 
 .72 
 
 
 2| x 2* x i 
 
 22.5 
 
 1.23 
 
 .54 
 
 .74 
 
 .49 
 
 .81 
 
 127 
 
 2^ x 2^ x i 
 
 2i x 2i- x -ft 
 
 10.6 
 
 17.8 
 
 .50 
 .79 
 
 .21 
 .34 
 
 .69 
 .67 
 
 .45 
 .44 
 
 .65 
 
 .72 
 
 128 
 
 2 x 2 x -fV 
 
 7 1 
 
 .27 
 
 .11 
 
 .62 
 
 .40 
 
 .57 
 
 
 2 x 2 x $ 
 
 13.6 
 
 .50 
 
 .21 
 
 .61 
 
 .39 
 
 .64 
 
 129 
 
 1| x 1J x A 
 
 6.2 
 
 .18 
 
 .08 
 
 .53 
 
 .36 
 
 .51 
 
 
 1| x 1| x i 
 
 11.7 
 
 .31 
 
 .14 
 
 .51 
 
 .35 
 
 .57 
 
 130 
 
 $4 X 1-f X 1% 
 
 5.3 
 
 .11 
 
 .05 
 
 .46 
 
 .31 
 
 .44 
 
 
 14 X 1 X 
 
 9.8 
 
 .19 
 
 .09 
 
 .44 
 
 .31 
 
 .51 
 
 131 
 
 H x 1\ x i 
 
 3.0 
 
 .05 
 
 .02 
 
 .41 
 
 .26 
 
 .36 
 
 
 H x li x i 
 
 5.6 
 
 .08 
 
 .04 
 
 .38 
 
 .26 
 
 .40 
 
 132 
 
 1 X 1 X i 
 
 2.3 
 
 .02 
 
 .01 
 
 .29 
 
 .20 
 
 .30 
 
 
 1 x 1 x i 
 
 4.4 
 
 .04 
 
 .02 
 
 .29 
 
 .20 
 
 .35 
 
 
 1 
 
 
 
 
 
 
 
ELEMENTS OP PENCOYD ANGLES. 
 
 99 
 
 \ 
 
 ELEMENTS OF 
 
 \ A 
 
 
 _ F -. PENCOYD ANGLES. 
 
 UNEVEN LEGS. 
 
 I. 
 
 II. 
 
 ni. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 IX. 
 
 X. 
 
 XI. 
 
 K 
 w 
 
 
 li 
 
 MOM. OF INERTIA. 
 
 RADII OF 
 GYRATION. 
 
 DlST. FROM 
 
 BASE TO 
 
 .NEUT.AXES 
 
 s 
 
 SIZE IN INCHES. 
 
 p 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 d. 
 
 
 3 
 
 
 
 A.B. 
 
 C. D. 
 
 E. F- 
 
 A. B. 
 
 C. D. 
 
 E. F. 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 140 
 
 6 x4 x-f fi 
 
 41.8 
 
 15.46 
 
 5.60 
 
 3.55 
 
 1.92 
 
 1.16 
 
 .92 
 
 1.96 
 
 .96 
 
 
 6 x 4 x 1 
 
 90.0 
 
 30.75 
 
 10.75 
 
 7.46 
 
 1.85 
 
 1.09 
 
 .91 
 
 2.17 
 
 1.17 
 
 141 
 
 5x4x| 
 
 32.3 
 
 8.14 
 
 4.66 
 
 2.47 
 
 1.59 
 
 1.20 
 
 .87 
 
 1.53 
 
 1.03 
 
 
 5x4x1 
 
 80.0 
 
 18.17 
 
 10.17 
 
 6.10 
 
 1.51 
 
 1.18 
 
 .86 
 
 1.75 
 
 1.25 
 
 142 
 
 5 x 3 x a. 
 
 30.5 
 
 7.78 
 
 3.23 
 
 1.95 
 
 1.60 
 
 1(3 
 
 .80 
 
 .61 
 
 .86 
 
 
 5 x 3^ x 
 
 58.1 
 
 13.92 
 
 5.55 
 
 3.72 
 
 1 55 
 
 '.98 
 
 .79 
 
 .75 
 
 1.00 
 
 143 
 
 5 x 3" x $ 
 
 28.6 
 
 7.37 
 
 2.04 
 
 1.42 
 
 1.61 
 
 .85 
 
 .70 
 
 .70 
 
 .70 
 
 
 5 x 3 x | 
 
 54.4 
 
 13.15 
 
 3.51 
 
 2.58 
 
 1.55 
 
 .80 
 
 .69 
 
 .84 
 
 .84 
 
 144 
 
 4* x 3 x i 
 
 86.7 
 
 5.50 
 
 1.98 
 
 1.27 
 
 1.44 
 
 .86 
 
 .69 
 
 .49 
 
 .74 
 
 
 4^ x 3 x t 
 
 43.0 
 
 8.44 
 
 2.98 
 
 2.04 
 
 1.40 
 
 .83 
 
 .68 
 
 1.58 
 
 .83 
 
 145 
 
 4 x 3J- x f 
 
 26.7 
 
 4.17 
 
 2.99 
 
 1.44 
 
 1.25 
 
 1.06 
 
 .74 
 
 1.20 
 
 .95 
 
 
 4 x:sf x f 
 
 43.0 
 
 6.37 
 
 4.52 
 
 2.34 
 
 1.22 
 
 1.03 
 
 .73 
 
 1.29 
 
 1.04 
 
 146 
 
 4 x 3 x f 
 
 24.8 
 
 3.96 
 
 1.92 
 
 1.10 
 
 1.26 
 
 .88 
 
 .67 
 
 1.28 
 
 .78 
 
 
 4x3x1- 
 
 89 8 
 
 6.03 
 
 2.87 
 
 1.69 
 
 1.23 
 
 .85 
 
 .65 
 
 1.37 
 
 .87- 
 
 147 
 
 3 x 3 x J 
 
 81.2 
 
 2.53 
 
 1.72 
 
 .86 
 
 1.09 
 
 .90 
 
 .64 
 
 1.07 
 
 .82 
 
 
 3i x 3 x 
 
 36.7 
 
 4.11 
 
 2.81 
 
 1.49 
 
 1.06 
 
 .87 
 
 .64 
 
 1.17 
 
 .92 
 
 148 
 
 3 x 2fc x ft 
 
 16.2 
 
 1.42 
 
 .90 
 
 .47 
 
 .94 
 
 .74 
 
 .54 
 
 .93 
 
 .68 
 
 
 3 x 2i x i 
 
 25.0 
 
 2.08 
 
 1.30 
 
 .72 
 
 .91 
 
 .72 
 
 .54 
 
 1.00 
 
 .75 
 
 149 
 
 ,3 x 2 x i 
 
 11.9 
 
 1.09 
 
 .39 
 
 .25 
 
 .96 
 
 .68 
 
 .4(5 
 
 .9 
 
 .49 
 
 
 |3 x 2 x i 
 
 22.5 
 
 1.92 
 
 .67 
 
 .47 
 
 .92 
 
 .55 
 
 .46 
 
 1*08 
 
 .58 
 
 150 
 
 j3 x 2 x -fa 
 
 17.8 
 
 2.19 
 
 .94 
 
 .56 
 
 1.11 
 
 .73 
 
 .56 
 
 1.14 
 
 .64 
 
 
 [8| x 2j x 
 
 27.5 
 
 3.24 
 
 1.86 
 
 .87 
 
 1.08 
 
 .70 
 
 .56 
 
 1.20 
 
 .70 
 
 151 
 
 6 x 3i x & 
 
 39.6 
 
 14.76 
 
 3.81 
 
 2.68 
 
 1.93 
 
 .98 
 
 .82 
 
 2.06 
 
 .81 
 
 
 6 x 8i x 1 
 
 85.0 
 
 29.24 
 
 7.21 
 
 5.75 
 
 1.86 
 
 .92 
 
 .81 
 
 2.26 
 
 1.01 
 
 152 
 
 16^x4 xft 
 6 x 4 x 1 
 
 44.0 
 95.0 
 
 19.29 
 38.66 
 
 5.723.87 
 11.008.35 
 
 2.(i9 
 
 2.02 
 
 1.14 
 1.08 
 
 .94 
 .93 
 
 2.18 
 2.88 
 
 .93 
 1.18 
 
 153 
 
 5Jr X 3 X f 
 
 32.3 10.12 
 
 3.2712.14 
 
 1.77 
 
 1.05 
 
 .81 
 
 1.82 
 
 .82 
 
 
 5| x 3| x | 52.3 
 
 15.73 
 
 4.963.35 
 
 1.73 
 
 .97 
 
 .80 
 
 1.91 
 
 .91 
 
 154 
 
 7 x 3| x | 01.7 
 
 30.25 
 
 5.284.45 
 
 2.21 
 
 .92 
 
 .85 
 
 2.57 
 
 .82 
 
 
 7 x 3 x l||95.0 
 
 |45.37 
 
 7.536.70 
 
 2.19 
 
 .88 
 
 .84 
 
 2.71 
 
 .96 
 
 155 
 
 2 x 2 x i 
 
 110 6 
 
 .71 
 
 .37 
 
 .20 
 
 .81 
 
 .59 
 
 .43 
 
 .78 
 
 .54 
 
 
 2^ x 2 x | 
 
 20.0 
 
 1.09 
 
 .63 
 
 .3? 
 
 .74 
 
 .56 
 
 .43 
 
 .87 
 
 .62 
 
 156 
 
 2i x H x 1 3 6 
 
 6 7 
 
 .34 
 
 .13 
 
 .08 
 
 .71 
 
 .43 
 
 .34 
 
 .76 
 
 .38 
 
 
 8i x li x 2 
 
 12.6 
 
 .5( 
 
 .21 
 
 .15 
 
 .63 
 
 .40 
 
 .34 
 
 .82 
 
 .44 
 
 157 
 
 2 x 1* x A 
 
 5.7 
 
 .23 
 
 .07 
 
 .05 
 
 .63 
 
 .35 
 
 .31 
 
 .68 
 
 .31 
 
 
 2 x H x f 
 
 9.2 
 
 o. 
 
 .10 
 
 .08 
 
 .59 
 
 .33 
 
 .29 
 
 .70 
 
 .32 
 
100 
 
 WROUGHT IKON AND STEEL. 
 C 
 
 ELEMENTS OF 
 
 A x-B 
 
 PENCOYD TEES. 
 
 EVEN LEGS. 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 fc 
 
 H 
 O 
 
 70 
 
 SIZE IN INCHES. 
 
 WEIGHT PER 
 YARD. 
 
 MOMENTS OF 
 INERTIA. 
 
 KADII OF 
 GYRATION. 
 
 DISTANCE, </, 
 I"*" FROM BASE TO 
 ^ NEUTRAL Axis. 
 
 Axis 
 A. B. 
 
 Axis 
 C. D. 
 
 Axis 
 A. B. 
 
 Axis 
 C. D. 
 
 4 x 4 x 
 
 36.5 
 
 5.26 
 
 2.55 
 
 1.20 
 
 .84 
 
 71 
 
 3 x 3 x B 
 
 31. 
 
 3.47 
 
 1.70 
 
 1.06 
 
 .74 
 
 1.00 
 
 72 
 
 3 x 3 x M 
 
 26. 
 
 2.10 
 
 1.01 
 
 .90 
 
 .62 
 
 .90 
 
 73 
 
 2* x 2|- x -ft 
 
 19.5 
 
 1.12 
 
 .58 
 
 .78 
 
 .55 
 
 -.75 
 
 74 
 
 2J x 2} x | 
 
 17.52 
 
 .97 
 
 .49 
 
 .75 
 
 .53 
 
 .75 
 
 75 
 
 21- x 21 x { 
 
 11.75 
 
 .52 
 
 .30 
 
 .65 
 
 .50 
 
 .61 
 
 76 
 
 21- x 21 x & 
 
 12. 
 
 .54 
 
 .27 
 
 .67 
 
 .47 
 
 .65 
 
 77 
 
 2 x 2 x & 
 
 10.5 
 
 .38 
 
 .19 
 
 .60 
 
 .43 
 
 .60 
 
 78 
 
 If x If x & 
 
 7.1 
 
 .21 
 
 .10 
 
 .54 
 
 .37 
 
 .50 
 
 79 
 
 U x 1* x A 
 
 6. 
 
 .13 
 
 .06 
 
 .46 
 
 .32 
 
 .45 
 
 80 
 
 n x 11 x v*. 
 
 4.5 
 
 .07 
 
 .04 
 
 .37 
 
 .27 
 
 .37 
 
 81 
 
 1 x 1 x A 
 
 3.0 
 
 .03 
 
 .02 
 
 .30 
 
 .26 
 
 .30 
 
 82 
 
 3 x 3 x M 
 
 19.3 
 
 1.59 
 
 .75 
 
 .91 
 
 .62 
 
 .84 
 
 83 
 
 8 x 8 x if 
 
 22.6 
 
 1.83 
 
 .89 
 
 .90 
 
 .63 
 
 .86 
 
ELEMENTS OF PENCOYD TEES. 
 C 
 
 101 
 
 ELEMENTS 
 
 UNEVEN LEGS. 
 
 TEES. 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 K 
 M 
 M 
 i 
 
 1 
 
 
 90 
 
 SIZE IN INCHES. 
 
 P 
 
 44.5 
 
 MOMENTS OP 
 INERTIA. 
 
 RADII OF 
 GYRATION. 
 
 fill 
 
 Axis 
 A. B. 
 
 Axis 
 C. D. 
 
 Axis 
 A. B. 
 
 Axis 
 C. D. 
 
 4ix3i 
 
 5.27 
 
 3.66 
 
 1.09 
 
 .91 
 
 1.16 
 
 91 
 
 4 x 3i 
 
 41.8 
 
 4.65 
 
 3.23 
 
 1.05 
 
 .88 
 
 1.09 
 
 92 
 
 5 x 2 
 
 30.7 
 
 1.61 
 
 4.01 
 
 .72 
 
 1.14 
 
 .67 
 
 93 
 
 5 x 2t 
 
 33.0 
 
 1.63 
 
 4.58 
 
 .70 
 
 1.17 
 
 .64 
 
 94 
 
 4x3 
 
 25.9 
 
 1.94 
 
 2.18 
 
 .86 
 
 .92 
 
 .77 
 
 95 
 
 4x3 
 
 25.25 
 
 2.09 
 
 1.69 
 
 .91 
 
 .82 
 
 .84 
 
 96 
 
 4x2 
 
 20.4 
 
 .68 
 
 1 68 
 
 .58 
 
 .91 
 
 .54 
 
 97 
 
 3 x 3| 
 
 28.25 
 
 3.12 
 
 1.06 
 
 1.05 
 
 .61 
 
 1.10 
 
 98 
 
 3 x 2 
 
 23.8 
 
 1.38 
 
 .94 
 
 .76 
 
 .63 
 
 .82 
 
 99 
 
 3 x 1^ 
 
 11.2 
 
 .19 
 
 .56 
 
 .41 
 
 .71 
 
 .37 
 
 100 
 
 at x H 
 
 9.1 
 
 .10 
 
 .33 
 
 .33 
 
 .60 
 
 .32 
 
 101 
 
 2 x li 
 
 8.75 
 
 .16 
 
 .18 
 
 .43 
 
 .45 
 
 43 
 
 102 
 
 2x1 
 
 7. 
 
 .05 
 
 .17 
 
 .26 
 
 .49 
 
 .27 
 
 103 
 
 2 x & 
 
 5.88 
 
 .01 
 
 .17 
 
 .13 
 
 .54 
 
 .17 
 
 104 
 
 2f x If 
 
 18.75 
 
 .56 
 
 .62 
 
 .55 
 
 .58 
 
 .66 
 
 105 
 
 21 x 2 
 
 21. 
 
 .83 
 
 .63 
 
 .63 
 
 .55 
 
 .75 
 
 106 
 107 
 
 5 x 3t 
 5x4 
 
 48.44 
 44.1 
 
 5.37 
 6.24 
 
 5.31 
 5.25 
 
 1.05 
 1.19 
 
 1.04 
 1.09 
 
 1.05 
 1.08 
 
 108 
 
 a x -ft 
 
 6.5 
 
 .01 
 
 .24 
 
 .12 
 
 .61 
 
 .18 
 
 109 
 
 4x4^ 
 
 38.5 
 
 7.26 
 
 2.70 
 
 1.37 
 
 .84 
 
 1.32 
 
 110 
 
 3 x 2 
 
 17.6 
 
 .94 
 
 .74 
 
 .73 
 
 .65 
 
 .69 
 
 111 
 
 3 x 2t 
 
 20.6 
 
 1.08 
 
 .so 
 
 .72 
 
 .66 
 
 .70 
 
102 WROUGHT IRON AND STEEL. 
 
 MOMENTS OF INERTIA. 
 
 The following formulae were used in calculating the moments 
 of inertia and radii of gyration of the various sections given in 
 the tables, pages 93-101. 
 
 When not otherwise specified the axis referred to passes 
 through the centre of gravity of the section, in a horizontal 
 position to the figure as shown. 
 
 I signifies moment of inertia. 
 A " total area of section. 
 R " radius of gyration. 
 
 d " distance from base to centre of gravity. 
 
 In all cases the radius of gyration = JL/ , and the moment of 
 
 resistan / x co-efficient for strength of material 
 
 ~~ distance from neutral axis to farthest edge of section* 
 
 SOLID RECTANGLE. 
 T _ bh 3 Ak* 
 
 = 13 = ~12' 
 r /, axis xy = -^-- 
 
 HOLLOW RECTANGLE OR I BEAM WITH PARALLEL FLANGES. 
 t 6 ^. f 64 
 
 -h --'W-t-i- /I * 
 
MOMENTS OF INERTIA. 
 
 SOLID TRIANGLE. 
 
 bh* 
 
 /, axis xy = - - 
 
 W* 3 
 
 J, axis uv = -H 
 o 
 
 SOLID CIRCLE. 
 
 1= . 
 
 .<_Air 
 : 16 ' 
 
 HOLLOW CIRCLE. 
 
 / = (outer radius 4 - inner radius 4 ) . 7854 
 
 SOLID SEMICIRCLE. 
 
 s jt*Z2: w /. axis xy = .3927r 4 = 
 d = .4244r. 
 
 SOLID ELLIPSE. 
 
 J= . 
 
104 
 
 WKOUGHT IKON AND STEEL. 
 TEE SECTION. 
 
 
 3 
 
 . 
 
 ~2A ' 
 
 L = 
 
 ANGLE SECTION. 
 
 tc* + bd* -(b-t)(d- t) 3 
 
 For even or 
 
 uneven angles. 
 /, axis * = *(* 
 
 6 N ^/ For uneven angles. 
 xy passes through centre of gravity parallel to ee. 
 
 -(--4)7 
 
 Foreven 
 
 angles. 
 A close approximation for the latter is the following : 
 
 I, axis xy = . For even angles. 
 
 ^5 
 
 /, axis xy = js For uneven an 
 
 ,, 
 = 
 
 t(tf-t*) 
 -JJ-T- -. For even and uneven an- 
 
 aJL 
 
 
 
 . For uneven angles. 
 
MOMENTS OF INERTIA. 
 
 105 
 
 In even angles radius of gyration around xy = two-thirds (f) 
 of the radius of gyration around horizontal axis. 
 
 In uneven angles the distance from centre of gravity in direc- 
 tion of the long leg exceeds that in the direction of the short leg 
 by half the difference in the length of the two legs. 
 
 I BEAM SECTION. 
 
 8 = taper of flange. 
 
 cs* 
 
 b - 
 
 *-^S* J,axiS*y = - 6 -+ i 2.+ -~ 
 
 b t 
 
 CHANNEL SECTION. 
 
 s taper of flange. 
 
 r 
 
 
 l-t' 
 
 1= 
 
 12 
 
 2mb 3 + If 
 
 axis xy = 
 
 d = 
 
 3 
 
106 WEOUGHT IEON AND STEEL. 
 
 DECK BEAM SECTION. 
 
 * = taper of flange. a = area of bulb. 
 
 o = m - . 
 3 
 
 86 
 
 nf 
 
 a (2 h - ) + t (h - k'f + (b - t) p*+ s(l-t) (p + - 
 
 
 In the table of elements, pages 92-101, the moments of inertia 
 and radii of gyration are given for the minimum section of each 
 shape but the moment of inertia, for any increased section can 
 readily be ascertained as follows, without recalculating the 
 whole. 
 
 FOB ANY I BEAM, CHANNEL BAR OR DECK BEAM. 
 
 AXIS PERPENDICULAR TO WEB. 
 
 Let a = increase of area in square inches over minimum sec- 
 tion given in the table. Let d depth (size) of beam, then 
 
 is the moment of inertia for increase of area, which added to 
 
 1,0 
 
 tabular figures gives the correct result for the enlarged section. 
 Example. A 12" I Beam, No. 4, area 12 square inches, is in- 
 
 O y 1 O 2 
 
 creased to 14 square inches. - ^- = 24, which added to the 
 
 moment given in col. 7272.86 + 24 = 296.86, the moment of 
 inertia desired. 
 
MOMENTS OF INERTIA. 107 
 
 /272 8fi 
 
 Radius of gyration of the former A/ =4.78 inches. 
 
 ' 12 
 
 A>Qfi ftfi 
 
 Radius of gyration of the latter y ^- go =4.60 inches. 
 
 The radius of gyration will be found to alter very little, and 
 for all practical purposes, the tabular figures may be accepted 
 within the range of section possible for each shape. 
 
 The above is only a close approximation for deck beams. 
 
 FOR ANY I BEAM OR DECK BEAM. 
 
 AXIS PARALLEL WITH WEB. 
 
 The following rule gives a close approximation for the mo- 
 ment of inertia. 
 
 Multiply the increase of area in square inches by the total 
 thickness of web in the enlarged section. This product added 
 to the tabular number in col. 8, will give the moment of inertia 
 for the enlarged section. 
 
 Example. A 10" I Beam, No. 8, area 9 square inches is in- 
 creased to 10f square inches, having a web thickness of .525 
 inches. . 525 x l = . 7875, which added to the amount in col. 
 VIII., 8.09 + .78 = 8.87, the moment of inertia required. 
 
 Radius of gyration of least section = A/ _ = . 95 inches. 
 
 f 9 
 
 Radius of gyration of enlarged section = 4/ =.92 inches. 
 
 ' 10.5 
 
 The radius of gyration alters but very little, and may be ac- 
 cepted as practically unchanged within the limits that any shape 
 can be increased. 
 
 CHANNELS. 
 
 For channels, in relation to axis parallel to web the moment 
 of inertia increases nearly in a direct ratio to the increase of 
 sectional area, but not precisely so, this ratio being too great for 
 the larger sections and too little for the smaller sizes of channel 
 bars. 
 
 The radius of gyration alters but little as the sectional area is 
 
108 WKOUGHT IKON AND STEEL. 
 
 changed, and practically may be accepted as unchanged within 
 the range of variation possible for any particular size. 
 
 The distance d will not vary sufficiently in any section be- 
 tween the limits of minimum and maximum to make any prac- 
 tical difference in ordinary calculations where it may be used. 
 
 ANGLES. 
 
 For angles referring to any axis passing through the centre of 
 gravity, the inertia increases nearly in the same ratio as the area 
 increases. Our table gives values of / for the minimum and 
 maximum sections ; any intermediate section can be obtained by 
 proportion unless great accuracy is required. Our tables ex- 
 hibit the change in values of R between the least and greatest 
 sections, which in the case of small angles remain practically 
 unaltered within the range of possible variation of area. 
 
 INERTIA OF COMPOUND SHAPES. 
 
 " The moment of inertia of any section about any axis is equal 
 to the /about a parallel axis passing through its centre of grav- 
 ity + the area of the section multiplied by the square of the 
 distance between the axes." 
 
 By use of this rule the moments of inertia or radii of gyration 
 of any single sections being known, corresponding values can 
 readily be obtained for any combination of these sections. 
 
 TV^js i 
 
 i.i-\-T msia Example No. 1. A combination of two 9" 
 54 Ib. Channels, and two 12 x { plates as 
 shown. 
 
 fc ;/ I >H AXIS A B OF SECTION. 
 
 /for B 2 channels, col. VII, page 94, = 128.680 
 
 / for 2 plates = i?_^ i?2! x 2 = . 03125 ) 
 
 r 
 6 (area of plates) x 4f a = 128 . 34375 ) = 128 . 375 
 
 /for combined section = 257.055 
 
 which divided by area (14) gives 18.3611 - R 2 or 4.285 radius of 
 combined section. 
 
MOMENTS OF INERTIA. 109 
 
 AXIS C D. 
 
 Find distance d = (.67) from col. XV., page 95, then obtaining 
 the distance (4.2325) between axes CD and EF. 
 
 /for 2 channels around axis JZFfrom col. VIII., = 4.94 
 Area of channels x square of distance = 10.8 x 4.2325' = 193.471 
 
 / for 2 plates =' 5 * 123 = 72. 
 
 / for combined section 270 . 41 1 
 
 Radius of gyration = j/ 270 ' 411 =4.395. 
 
 By similar methods, inertia or radius of gyration for any com- 
 bination of shapes can readily be obtained. 
 
 Example No. 2. A " built-up beam " composed of : 
 
 ~~ >!l " 4 angles 3" x 3" x \". 
 
 2 plates 8" x |". 
 1 plate 15" x F. 
 
 AXIS A B. 
 
 /of two 8" x | plates = 9 * ^ x 2 = .167 
 
 + 8 (area) x 7f (sq. of distance d) =480.5 
 
 480.667 
 
 /of one 15" x |" plate = ^^= 105.469 
 
 /of four 3 x 3 x i angles = 4 x 1 .24 (see col. \ 
 
 IV, page 98), = 4.96 } 
 
 + 5.7" (area) x 6.66 2 (sq. of distance d 1 ) =255.045* 
 
 260.005 
 
 Inertia of combined section around A B = 846 . 141 
 
 846.141 
 
 _ ,. .. 7846.141 
 
 Radius of gyration =|/ -jg-g-^ = 6 - 
 
 61 - 
 
110 WROUGHT IRON AND STEEL. 
 
 AXIS C. D. 
 
 lot two 8 x \ plates =^jj^ x 2 = 42.667 
 
 I of one 15 x | plate = ^^- = .066 
 
 La 
 
 lot four 3 x 3 x angles = 4 x 1.24 (see 
 
 col. IV, page 98) 
 + 5 . 75 (area) x 1 . 0275 2 (sq. of distance d") 
 
 - 11.031 
 
 ee \ 
 
 = 4.96 t 
 d" = 6 . 071 ) 
 
 Inertia of combined section around C D = 53 . 764 
 
 Radius of gyration = V 53 - 764 = 1 . 66. 
 ' 19 . 375 
 
 RADIUS OF GYRATION OF COMPOUND SHAPES. 
 
 In the case of a pair of any shape without a web the value of 
 It can always be readily found without considering the moment 
 of inertia. 
 
 The radius of gyration for any section around an axis parallel 
 to another axis passing through its centre of gravity, is found 
 as follows : 
 
 Let r = radius of gyration around axis through centre of grav- 
 ity. R radius of gyration around another axis parallel to 
 above, d distance between axes. 
 
 "When r is small, R may be taken as equal to d without mate- 
 rial error. Thus in the case of a pair of channels latticed to- 
 gether, or a similar construction. 
 
 Example No. 1. Two 9" 54 Ib. channels placed 4.66" apart, 
 E E required the radius of gyration around axis CD 
 l-j ^ for combined section. 
 
 Find r on col. X., page 95, = .68 and r 2 = .4624. 
 Find distance from base of channel to neutral axis 
 col. XV., same page, = .07, this added to \ distance 
 between the two bars, 2.33"= 3" = d, and d* 9. 
 Radius of gyration of the pair as placed equals, 
 
MOMENTS OF INEETIA. Ill 
 
 The value of J? for the whole section in relation to the axis A 
 B is the same as for the single channel, to be found in the 
 tables. 
 
 Example No 2. Four 3" x 3" x f" angles placed as shown; 
 form a column 10 inches square; required the 
 i 8 y,radius of gyration. 
 
 Find T OQ C0i> VI) P age 98 ' = - 91 ' atld ? ' 2 ~ 
 
 -8281. 
 
 Find distance from side of angle to neutral 
 P| f\ axis, coi. VII. , same page, = . 89. Subtract this 
 
 I i _ t j | from | the width of column =5. .89 = 
 
 p 4.11 = d or distance between two axes, d 2 = 
 
 16.8921. 
 Radius of gyration of 4 angles as placed = 
 
 -i*" 3 ""! I?* s _ i 8 
 
 I'M 
 IJi 11 
 
 _ 
 
 -Y/16.8921 + .8281 =4.21. 
 
 When the angles are large as compared with the outer dimen- 
 sions of the combined section, the radius of gyration can be 
 taken without serious error from the table of radii of gyration 
 for square columns, on page 155. 
 
112 
 
 WROUGHT IRON AND STEEL. 
 
 O O Q 
 
 
 
 sil 
 
 i 
 
 
 fc ^ 
 
 M 
 
 * * 
 
 "*^ -i 
 
 h 
 
 
 ill 
 
 o 
 
 
 
 
 g 
 
 r S - 
 
 g| g 
 
 ^S 
 5 |* 
 
 s 
 a 
 
 |* j 
 
 
 1 
 
 ""v ' 
 
 ^aS 
 
 s 
 
 
 ^ II 
 
 RATION. 
 
 
 h-H CC ^ O 
 
 H 
 
 * * 
 
 ^J ^ ^ 
 
 
 
 * * 
 
 
 fc 
 
 
 A^ '_|j _ 
 
 o 
 
 % *b e. 
 
 htaJ ^ ^* * 
 
 9 
 
 
 
 p 
 
 
 rh >-> P 
 ^o.S 
 
 O O <33 
 
 5 
 H 
 
 t3 + iH S + ^ ^ 
 
 ' S c* ^ ^o ^ P^ 
 
 ill! 
 
 IB 
 
 S 
 
 fo 
 
 e g e? S 
 
 S ^nS'.S 
 
 
 
 ^ ^ ^ 
 
 S J^'s 
 
 3 
 
 
 p 1 ^ 
 
 p 
 
 
 ^5.2^ 
 
 
 
 
 o"s i 
 
 
 
 1 P" 8 
 
 
 S3 8 g ri 
 
 'S O >-, 
 
 
 i ill PI ill i 
 
 ^ ""o 
 
 
 i * * S o 
 
 ^5 ^ 
 
 A 
 
 o 
 
 $ g o| 8 ^ |s 5 
 
 M t-i "P 
 
 1 
 
 
 
 g S.2 11 M 
 
 8|i 
 
 h 
 
 9 ^ea o B22 w 
 
 
 O 
 
 o a ii ii w B i i (2 
 
 - J I 
 
 s 
 
 t" ^ p ^ 
 
 lit 
 
 i 
 
 
 in 
 
 
 n S O O 
 
RADIUS OF GYRATION. 
 
 113 
 
 ! 
 
 1 
 
 1 
 
 1 
 
 j 
 
 1 
 
 
 c 
 
 1 
 
 V3 X 
 
 ^ J 
 
 ^ ^ 
 
 5 1 
 
 ! 1 
 
 
 
 W ^H 
 
 P 
 
 gj 
 
 
 01 
 
 'd 
 
 T3 
 
 | 
 
 "O 
 
 
 
 O 
 
 
 
 i 
 
 i 
 
 
 c 
 
 be 
 
 "8 
 
 a ? 
 
 -^ 
 
 a Ifi 
 
 > ' O 
 CO -i- 3 
 
 C 
 
 GQ *g 
 04 
 
 c3 
 
 , E 
 
 a | 
 
 I 
 
 T-l t^ 
 
 
 I 
 
 
 * M 
 
 9 
 
 
 
 c 
 
 
 TH g 
 
 
 
 ^ 
 
 1 
 
 
 
 
 d 
 
 
 s 
 
 ^ 
 
 
 
 
 1 
 
 
 00 
 
 s 
 
 hJ f 
 
 i 
 
 S J 3 w 
 
 p-l 
 
 J| 
 
 <H 
 
WROUGHT IRON AND STEEL. 
 
 ROLLED IRON STRUTS. 
 
 In the following consideration of rolled struts of various 
 shapes, the least radius of gyration of the cross section taken 
 around an axis through the centre of gravity is assumed as the 
 effective radius of the strut. The resistance of any section per 
 unit of area will in general terms vary directly as the square of 
 the least radius of gyration, and inversely as the square of the 
 length of the strut.* The shape of the section and the distribu- 
 tion of the metal to resist local crippling strains must also be 
 considered. As a rule, that shape will be strongest which pre- 
 sents the least extent of flat unbraced surface. For instance, 
 two M sections of unequal web widths may have the same web 
 thickness, the same flange area, and the same least radius of gy- 
 ration, but the wider webbed section will be the weaker per unit 
 of area, on account of the greater extent of unbraced web sur- 
 face it contains. For the same reason a hollow rectangular sec- 
 tion, composed of thin plates will be to some extent weaker than 
 a circular section of the same length having the same arta and 
 radius of gyration. 
 
 END CONNECTIONS. 
 
 As is well known, the method of securing the ends of the struts 
 exercises an important influence on their resistance to bending, 
 as the member is held more or less rigidly in the direct line of 
 thrust. 
 
 In the tables, struts are classified in four divisions, viz. : 
 " Fixed Ended," "Flat Ended," " Hinged Ended," and " Round 
 Ended." 
 
 In the class of " fixed ends" the struts are supposed to be so 
 rigidly attached at both ends to the contiguous parts of the 
 structure that the attachment would not be severed if the mem- 
 ber was subjected to the ultimate load. "Flat ended " struts 
 are supposed to have their ends flat and square with the axis of 
 length but not rigidly attached to the adjoining parts. " Hinged 
 
 * This applies only to long struts with free euds. 
 
ROLLED IRON STRUTS. 115 
 
 ends " embrace the class which have both ends properly fitted 
 with pins, or ball and socket joints, of substantial dimensions as 
 compared with the section of the strut ; the centres of these end 
 joints being practically coincident with an axis passing through 
 the centre of gravity of the section of the strut. " Round 
 ended " struts are those which have only central points of con- 
 tact, such as balls or pins resting on flat plates, but still the cen- 
 tres of the balls or pins coincident with the proper axis of the 
 strut. 
 
 If in hinged-euded struts the balls or pins are of comparatively 
 insignificant diameter, it will be safest in such cases to consider 
 the struts as round ended. 
 
 If there should be any serious deviation of the centres of round 
 or hinged ends from the proper axis of the strut, there will fee a 
 reduction of resistance that cannot be estimated without know- 
 ing the exact conditions. No formula has been written which 
 expresses with accuracy the resistance to compression for various 
 sections and for an extended range of lengths. It is doubtful if 
 any simple formula admitting of ready practical application can 
 be devised; in fact none is required, as the results of experiments 
 can be embodied in tables and diagrams in such a compact form 
 that their application to any length or section can be readily 
 made. 
 
 When the pins of hinged-end struts are of substantial diam- 
 eter, well fitted, and exactly centred, experiment shows that the 
 hinged ended will be equally as strong as flat ended struts. 
 
 But a very slight inaccuracy of the centring rapidly reduces 
 the resistance to lateral bending, and as it is almost impossible 
 in practice to uniformly maintain the rigid accuracy required, 
 it is considered best to allow for such inaccuracies to the extent 
 given in the tables, which are the average of many experi- 
 ments. 
 
 TABLES OF STRUTS. 
 
 In table No. 1, the first column gives the effective length of 
 the strut divided by the least radius of gyration of its cross sec- 
 tion, and the successive columns give the ultimate load per 
 square inch of sectional area for each of the four classes afore- 
 
116 WROUGHT IRON AND STEEL. 
 
 said. We mean by " ultimate load " that pressure under which 
 the strut fails. 
 
 These ultimate loads are the averages of a number of experi- 
 ments which we have recently made on carefully prepared spec- 
 imens, and are believed to be trustworthy. 
 
 For hinged-ended struts the figures apply to those cases in 
 which the axis of the pin is at right angles to the least radius of 
 gyration, or in which the strut is free to rotate on the pin in its 
 weakest direction. If the pin should be placed in another direc- 
 tion, or if the strut should be secured from failure in its weakest 
 direction, there will be a correction for determining the resist- 
 ance as hereafter described. 
 
 FACTORS OF SAFETY. 
 
 It is considered good practice to increase the factors of safety 
 as the length of the strut is increased, owing to the greater in- 
 ability of the long struts to resist cross strains, etc. For similar 
 reasons we consider it advisable to increase the factor of safety 
 for hinged and round ends in a greater ratio than for fixed or 
 flat ends. 
 
 Presuming that one-third of the ultimate load would consti- 
 tute the greatest safe load for the shortest struts, the following 
 progressive factors of safety are adopted for the increasing 
 lengths. 
 
 3. + .01 for flat and fixed ends. 
 r 
 
 3 + .015 for hinged and round ends. 
 r 
 
 I = length of strut. 
 r least radius of gyration. 
 From the above we derive the following table : 
 
EOLLED IKON STRUTS. 
 
 117 
 
 FACTORS OF SAFETY. 
 
 
 R * 
 
 P r\ 
 
 
 Pa 
 
 R 03 ' 
 
 
 R ' 
 
 R g' 
 
 
 X O 
 
 Z 
 
 
 X R 
 
 fe " 
 
 
 X R 
 
 
 
 I 
 
 
 
 w 
 
 I 
 
 < 
 
 *& 
 
 I 
 
 ^H 
 
 21 
 
 T 
 
 W H 
 
 w R 
 
 T 
 
 ta H. 
 
 Sg 
 
 T 
 
 W H 
 
 gg 
 
 
 
 
 2 o 
 
 
 
 
 II 
 
 
 I 2 
 
 K| 
 
 
 
 EE 
 
 
 
 
 
 
 WK 
 
 20 
 
 3.2 
 
 3.3 
 
 150 
 
 4.5 
 
 5.25 
 
 280 
 
 5.8 
 
 7.2 
 
 30 
 
 3.3 
 
 3.45 
 
 160 
 
 4.6 
 
 5.4 
 
 290 
 
 5.9 
 
 7.35 
 
 40 
 
 3.4 
 
 3.6 
 
 170 
 
 4.7 
 
 5.55 
 
 300 
 
 6.0 
 
 7.5 
 
 50 
 
 3.5 
 
 3.75 
 
 180 
 
 4.8 
 
 5.7 
 
 310 
 
 6.1 
 
 7.65 
 
 60 
 
 3.6 
 
 3.9 
 
 190 
 
 4.9 
 
 5.85 
 
 320 
 
 6.2 
 
 7.8 
 
 70 
 
 3.7 
 
 4.05 
 
 200 
 
 5.0 
 
 6.0 
 
 830 
 
 (5.3 
 
 7.95 
 
 80 
 
 3.8 
 
 4.2 
 
 210 
 
 5.1 
 
 6.15 
 
 340 
 
 6.4 
 
 8.1 
 
 90 
 
 3.9 
 
 4.35 
 
 220 
 
 5.2 
 
 6.3 
 
 350 
 
 6.5 
 
 8.25 
 
 100 
 
 4.0 
 
 4.5 
 
 2:50 
 
 5.3 
 
 6.45 
 
 360 
 
 6.6 
 
 8.4 
 
 110 
 
 4.1 
 
 4.65 
 
 240 
 
 5.4 
 
 6.6 
 
 370 
 
 6.7 
 
 8.55 
 
 120 
 
 4.2 
 
 4.8 
 
 250 
 
 5.5 
 
 6.75 
 
 880 
 
 6.8 
 
 8.7: 
 
 130 
 
 4.3 
 
 4.95 
 
 260 
 
 5.6 
 
 6.9 
 
 390 
 
 6.9 
 
 8.85 
 
 140 
 
 4.4 
 
 5.1 
 
 270 
 
 5.7 
 
 7.05 
 
 400 
 
 7.0 
 
 9.0 
 
 Table No. 2 represents the greatest safe load per square inch 
 of section for each of the four classes of struts and is derived 
 from the results in Table No. 1 by means of the foregoing fac- 
 tors of safety. 
 
 The remarks on page 33 for safe loads on beams, apply also to 
 struts. The loads in Table No. 2 ought to be applied only 
 under the most favorable circumstances, such as an invariable 
 condition of the load, little or no vibration, etc. Under cer- 
 tain conditions, such as for buildings, bridges, etc., the least 
 factor of safety ought to be four (4), which would increase each 
 factor in the above table by unity. The safe load will then be 
 found by dividing the results given in Table No. 1 by the cor- 
 rected factor of safety. 
 
118 WROUGHT IEON AND STEEL. 
 
 No. 1. 
 WROUGHT IRON STRUTS. 
 
 ULTIMATE PRESSURE IN LBS. PER SQUARE INCH. 
 
 LENGTH 
 
 FLAT 
 
 FIXED 
 
 HINGED 
 
 ROUND 
 
 LEAST RADIUS 
 OF GYRATION. 
 
 ENDS. 
 
 ENDS. 
 
 ENDS. 
 
 ENDS. 
 
 20 
 
 46.000 
 
 46,000 
 
 46,000 
 
 44,000 
 
 80 
 
 43,000 
 
 43,000- 
 
 43,000 
 
 40,250 
 
 40 
 
 40.000 
 
 40,000 
 
 40,000 
 
 36,500 
 
 50 
 
 3H,000 
 
 38.000 
 
 38,000 
 
 33,500 
 
 60 
 
 36,000 
 
 36,000 
 
 3o,UOO 
 
 3a,5>0 
 
 70 
 
 34,000 
 
 34,000 
 
 33,750 
 
 27,750 
 
 80 
 
 32,000 
 
 3-2,000 
 
 31,500 
 
 25,000 
 
 90 
 
 30,900 
 
 31.000 
 
 29,750 
 
 22,750 
 
 100 
 
 29,800 
 
 30,000 
 
 28,000 
 
 20.500 
 
 110 
 
 23,050 
 
 29,000 
 
 26,150 
 
 18,500 
 
 120 
 
 26,300 
 
 28,000 
 
 24.300 
 
 16500 
 
 130 
 
 24.900 
 
 26,750 
 
 22,650 
 
 14.G50 
 
 140 
 
 23,500 
 
 25,500 
 
 21,000 
 
 12,800 
 
 150 
 
 21,750 
 
 24,250 
 
 18,750 
 
 11,150 
 
 160 
 
 20,000 
 
 23,000 
 
 16,500 
 
 9,5 
 
 170 
 
 18,4: K) 
 
 21,500 
 
 14,650 
 
 8,500 
 
 180 
 
 16,800 
 
 20,000 
 
 12,800 
 
 7,500 
 
 190 
 
 15.650 
 
 18,750 
 
 11,800 
 
 6.750 
 
 200 
 
 14.500 
 
 17,500 
 
 10.800 
 
 6,000 
 
 210 
 
 13,600 
 
 16.250 
 
 9.800 
 
 5,500 
 
 220 
 
 12,700 
 
 15,000 
 
 8.800 
 
 s.noo 
 
 230 
 
 11,950 
 
 14,000 
 
 8.150 
 
 4,650 
 
 240 
 
 11,200 
 
 13,000 
 
 7.500 
 
 4,300 
 
 250 
 
 10,500 
 
 12,000 
 
 7,000 
 
 4,050 
 
 260 
 
 9,800 
 
 11,000 
 
 6,500 
 
 3,800 
 
 270 
 
 9,150 
 
 10,500 
 
 6.100 
 
 3.500 
 
 280 
 
 8,500 
 
 10,000 
 
 5,700 
 
 3,200 
 
 290 
 
 7,850 
 
 9,500 
 
 5.350 
 
 3,01)0 
 
 300 
 
 7,200 
 
 9000 
 
 5.000 
 
 2.800 
 
 310 
 
 6,600 
 
 8,500 
 
 4,750 
 
 2.650 
 
 320 
 
 6,000 
 
 8.000 
 
 4,500 
 
 2,500 
 
 330 
 
 5,550 
 
 7,500 
 
 4,2.50 
 
 2,300 
 
 340 
 
 5,100 
 
 7,000 
 
 4,000 
 
 2.100 
 
 350 
 
 4,700 
 
 6,750 
 
 3.750 
 
 2,000 
 
 360 
 
 4,300 
 
 6,500 
 
 3500 
 
 1,900 
 
 370 
 
 3.900 
 
 6.150 
 
 3.250 
 
 1,800 
 
 380 
 
 3.500 
 
 5.800 
 
 3,000 
 
 1,700 
 
 390 
 
 3,250 
 
 6,800 
 
 2,750 
 
 1,600 
 
 400 
 
 3,000 
 
 5,200 
 
 2.500 
 
 1,500 
 
 410 
 
 2750 
 
 5,0(10 
 
 2,400 
 
 1,400 
 
 420 
 
 2.500 
 
 4.800 
 
 2.300 
 
 1,300 
 
 430 
 
 2,.350 
 
 4.550 
 
 2.200 
 
 
 440 
 
 2,200 
 
 4.300 
 
 2,100 
 
 
 450 
 
 2,100 
 
 4,050 
 
 2,000 
 
 
 460 
 
 2,000 
 
 3,8CO 
 
 1,900 
 
 
 470 
 
 1,950 
 
 
 1,850 
 
 
 480 
 
 1,900 
 
 
 1,800 
 
 
WROUGHT IRON STEUTS. 
 
 119 
 
 No. 2. 
 GREATEST SAFE LOADS ON STRUTS. 
 
 Greatest safe load in Ibs. per square inch of cross section *or vertical struts. 
 Both ends are supposed to be secured as indicated at the head of each col- 
 umi?.. If both ends are not secured alike, take a mean proportional between 
 the values given for the classes to which each end belongs. If the strut is 
 hinged by any uncertain method so that the centres of pins and axis of strut 
 may not coincide, or the pins may be relatively small and loosely fitted, it is 
 best in such cases to consider the strut as " round ended." 
 
 LENGTH 
 
 FLAT 
 
 FIXED 
 
 HINGED 
 
 ROUND 
 
 LEAST RADIUS 
 OP GYRATION. 
 
 ENDS. 
 
 ENDS. 
 
 ENDS. 
 
 ENDS. 
 
 20 
 
 30 
 
 14,380 
 13,030 
 
 14.380 
 13,' 30 
 
 13,940 
 12,460 
 
 13,330 
 11,670 
 
 40 
 
 11,760 
 
 11,760 
 
 11.110 
 
 10.140 
 
 50 
 
 10,860 
 
 10,860 
 
 10,130 
 
 8,930 
 
 60 
 
 10,000 
 
 10,000 
 
 9,230 
 
 7,820 
 
 70 
 
 9,190 
 
 9.190 
 
 8,330 
 
 6,850 
 
 80 
 
 8,420 
 
 8,420 
 
 7,500 
 
 5,950 
 
 90 
 
 7,920 
 
 7,950 
 
 6,840 
 
 5,230 
 
 100 
 
 7,450 
 
 7,500 
 
 6,220 
 
 4,560 
 
 110 
 
 6,840 
 
 7.070 
 
 5.620 
 
 3,980 
 
 . 120 
 
 6,260 
 
 6,670 
 
 5.060 
 
 3,440 
 
 130 
 
 5, '.90 
 
 6,220 
 
 4.580 
 
 2,960 
 
 140 
 
 5,340 
 
 5,800 
 
 4,120 
 
 2,510 
 
 150 
 
 4,830 
 
 5,390 
 
 3.570 
 
 2,120 
 
 160 
 
 4,350 
 
 5,000 
 
 3,060 
 
 1,760 
 
 170 
 
 3,920 
 
 4,570 
 
 2,640 
 
 1,530 
 
 180 
 
 3,500 
 
 4.170 
 
 2,250 
 
 1,310 
 
 190 
 
 3,190 
 
 3,830 
 
 2,020 
 
 1,150 
 
 200 
 
 2,900 
 
 3,500 
 
 1,800 
 
 1,000 
 
 210 
 
 2,<;70 
 
 3,190 
 
 1,590 
 
 890 
 
 220 
 
 2,440 
 
 2.880 
 
 1,400 
 
 790 
 
 230 
 
 2,250 
 
 2.G40 
 
 1,260 
 
 720 
 
 240 
 
 2,070 
 
 2,410 
 
 1,140 
 
 650 
 
 250 
 
 ,910 
 
 2,180 
 
 1,040 
 
 600 
 
 260 
 
 ,750 
 
 1.960 
 
 940 
 
 550 
 
 270 
 
 ,610 
 
 1,S40 
 
 870 
 
 500 
 
 280 
 
 ,460 
 
 1,720 
 
 790 
 
 440 
 
 290 
 
 ,330 
 
 1,610 
 
 730 
 
 410 
 
 300 
 
 1,200 
 
 1,500 
 
 670 
 
 370 
 
 310 
 
 ,080 
 
 1,390 
 
 620 
 
 350 
 
 320 
 
 970 
 
 1,290 
 
 580 
 
 320 
 
 830 
 
 880 
 
 1,190 
 
 540 
 
 290 
 
 340 
 
 800 
 
 IJ'90 
 
 490 
 
 260 
 
 350 
 
 720 
 
 1,040 
 
 450 
 
 240 
 
 360 
 
 650 
 
 980 
 
 420 
 
 230 
 
 370 
 
 580 
 
 920 
 
 380 
 
 210 
 
 380 
 
 510 
 
 850 
 
 340 
 
 200 
 
 890 
 
 470 
 
 800 
 
 310 
 
 80 
 
 400 
 
 430 
 
 740 
 
 280 
 
 70 
 
120 WKOUGHT IRON AND STEEL. 
 
 ROLLED STRUCTURAL SHAPES AS STRUTS. 
 
 The following tables for the working values of various rolled 
 structural shapes as struts are derived directly from Table No. 
 2. The radii of gyration are taken from Tables of Elements, 
 pages 92-101. In all cases the strut is supposed to stand verti- 
 cal. In short struts this distinction is immaterial, but when the 
 length becomes considerable, the deflection resulting from its 
 own weight, if horizontal, would seriously affect the stability of 
 the strut. 
 
 The tables are calculated for the minimum section of each 
 shape. For sections increased above the minimum the resist- 
 ance per square inch will dimmish. This amount can be accu- 
 rately determined by finding the correct radius of gyration for 
 the enlarged section as heretofore described. But within the 
 range of variation of section possible for any shape, the tables 
 may be accepted as practically correct. The head notes to the- 
 tables indicate the condition assumed for each class of Ft ruts. 
 If the pins should be placed otherwise than as described in the 
 tables, the strut may be either weaker or stronger, according to 
 circumstances, which have to be determined for any particular 
 case. This results from the fact that a pin-connected strut if 
 properly designed should be considered hinged ended, only in 
 the direction in which it is free to rotate on the pin. 
 
 'In the direction of the axis of the pin it can be treat ed as a 
 " flat ended " strut. An I beam strut of the character described 
 in Tables 3, 4, and 5, braced laterally in the direction of its 
 flanges should be considered also by Tables 6, 7, and 8, as a 
 series of short struts whose lengths, are the distances between 
 points of bracing, and liable to fail in the direction of the 
 flanges. 
 
 Example. An 8" 65 Ib. I beam, 18 feet long is used as a strut 
 having pins at both ends at right angles to web. It would then 
 be flat ended in the direction of the- flanges, and by Table No. 
 7 the greatest safe load 1,990 Ibs. per square inch of section. 
 If braced in the direction of the flanges at two points 6 feet 
 apart it should then be considered as a series of flat ended struts 
 C feet long, whose safe load by Table No. 7, would be 8,320 Ibs. 
 per square inch. 
 
CHANNEL STRUTS. 121 
 
 In the direction of its web it remains a hinged-ended strut 18 
 feet long, and safe load by Table No. 4 8,690 Ibs. per square 
 inch. 
 
 CHANNEL STRUTS. 
 
 The foregoing remarks apply also to channels, which are seldom 
 used individually as struts, but frequently in pairs. When so 
 used, if the methods of connection are not of such a nature as to 
 insure the unity of action of the pair, they should be treated as 
 an assemblage of separate struts . But if connected by a proper 
 system of triangular latticing, the pair can be considered as a 
 unit, and each channel treated as a series of short struts whose 
 length is the distance between centres of latticing. 
 
 Example. A pair of 9" 54 Ib. channels, separated, etc., as 
 described on page 110, are connected by triangular latticing, 
 forming a hinged-ended strut 10 feet between pin centres. WLat 
 is the greatest safe load, and how far can latticing be spaced ? 
 
 As described on page 95, radius of gyration around axis across 
 the web of channel, or in the direction of the pin = 3 . 45 inches. 
 Eadius of gyration in opposite direction = 3.07 inches. Least 
 radius of gyration for a single channel = . 68 inch. 
 
 for hinged-ended direction = 35, and by Table No. 2 Safe 
 
 Load =11, 800 Ibs. for flat-ended direction = 39, and by same 
 T 
 
 table greatest safe load = 11,900 Ibs. 
 
 For each single channel the greatest length between latticing 
 = radius of gyration x 39 = 26| inches. 
 
 It is customary and is also good practice to reduce the dis- 
 tance between lattice centres below v'liat the above calculation 
 would require. 
 
 Tables Nos. 12-14, give the greatest safe loads per square 
 inch of sectional areas, for struts composed of a pair of channels 
 properly connected together, so as to insure unity of action. The 
 figures are derived from Table No . 2. 
 
 The distances D or d, for channels placed flanges inward or 
 flanges outward respectively, make the radii of gyration equal 
 lor either direction of axis. 
 
 These distances should not be diminished, and may be ad van- 
 
122 
 
 WROUGHT IRON AND STEEL. 
 
 tageously increased, especially for hihged-ended struts, if the pin 
 is placed parallel to the webs of the channels. These tables are 
 calculated for the standard minimum section of each channel. 
 The distance d may be slightly diminished for sections heavier 
 than the minimum, but the diminution can be so little that it is 
 practically unnecessary to notice it. Under each length of struts 
 in the table I represents the greatest distance apart in feet that 
 centres of lateral bracing can be spaced, without allowing weak- 
 ness in the individual channels. The distance I is obtained as 
 
 shown in last example, that is, by making = 
 
 T Mi 
 
 I = length between bracing. 
 L = total length of strut. 
 
 T = least radius of gyration for a single channel. 
 JB = least radius of gyration for the whole section. 
 
STEEL STKUTS. 123 
 
 STEEL STRUTS. 
 
 A table for the ultimate resistance of flat-ended struts of two 
 grades of steel will be found on page 31. These grades prob- 
 ably embrace the extremes of the material, that is, the hardest 
 and softest steels that are likely to be used in struts. 
 
 Experiments on this material are not sufficiently complete to 
 warrant a full statement of resistances of the various grades, 
 and for the various conditions of the strut, such as the methods 
 of connecting the ends, etc. 
 
 It is probable, however, that the relations existing between 
 the four classes of wrought-iron struts, as given in the following 
 tables, will also prevail in the same ratios for steel. The safe 
 loads for steel struts of any section or length, can therefore be 
 obtained by increasing the figures in the following tables, for 
 
 any ratio of , in the proportions given on page 81, as existing 
 T 
 
 between flat-ended struts of iron and steel. 
 
 When a grade of steel is used, intermediate in hardness be- 
 tween the mild and hard heretofore described, it is probable that 
 the strut resistance for such material may be safely approxi- 
 mated by simple proportion. 
 
 For instance, the steels referred to had carbon ratios of . 12 
 and .38 per cent, respectively. A mean proportion of these 
 would be .24 per cent. 
 
 It is probable that steel of latter grade would possess inter- 
 mediate compressive resistance between the two grades described 
 from our experiments. 
 
124: WROUGHT IKON AND STEEL. 
 
 No. 3. 
 
 PENCOYD I BEAMS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 When the struts are secure from failure in the direction of the flanges, and 
 can bend only in the direction of the web C D. Using factors of safety 
 given in previous tables. 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 BEAM. 
 
 OP 
 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 IK" 
 
 Fixed Ends.. . 
 
 
 14240 
 
 13700 
 
 13160 
 
 1-2650 
 
 12140 
 
 11670 
 
 11310 
 
 10950 
 
 L U 
 
 Flat Ends 
 
 14240 13700 13160 12650 12140 
 
 11670!! 1310 
 
 10950 
 
 Heavy 
 
 Hinged Ends... 
 
 13790 1 13200! 12610! 12050 11510 
 
 11010,10620 
 
 10230 
 
 I i = 5 Htt 
 
 Round Ends 
 
 
 13160 12500 11840 11210 10600 
 
 10020 9530 
 
 9050 
 
 ;, 
 
 Fixed Ends 
 
 
 14380 
 
 13840 
 
 13300 
 
 1278:) 
 
 12270 
 
 11760 
 
 11400 
 
 11040 
 
 -L t/ 
 
 Flat Ends 
 
 
 14380 1384 l 13300 12780 12270 
 
 11760 11403 
 
 11040 
 
 Light 6 _. 
 
 Hinged Ends... 
 
 
 13940 13350 12760 1 '21 90 1 1650 
 
 1111010720 
 
 10330 
 
 
 Round Ends. 
 
 13*30 
 
 12670 12000 11360 10750 101401 9660 
 
 9170 
 
 1 9" 
 
 Fixed Ends 
 
 | 
 
 14380J13570 
 
 12900 
 
 12270 
 
 11670 
 
 11220 
 
 10770 
 
 10340 
 
 9920 
 
 L _j 
 
 Heavy 
 
 Flat Ends 
 Hinged Ends... 
 
 1438013570 
 13940 i 13050 
 
 12900 12270 11670 11220 10770 10:340 
 123201 1 1 650 ! 1 1010 10520 10040 9590 
 
 9920 
 9140 
 
 r = 4-69 
 
 Round Ends 
 
 13330 
 
 12330 
 
 11520 
 
 10750 
 
 10020 
 
 9410 8820 
 
 8260 
 
 7720 
 
 1 9" 
 
 Fixed Ends.... 
 
 14380 
 
 13700 
 
 13030 
 
 12400 
 
 11760 
 
 11310' 10860 
 
 10430 
 
 10000 
 
 JL 
 
 Flat Ends 
 
 14880 
 
 13700 13030 12400, 11760 11310 108<>0 10430 
 
 10000 
 
 Light , 
 
 HiMgedEnds... 
 
 13940 
 
 13200 12460111780 11110 106-20 10130 
 
 9680 
 
 9230 
 
 I 4-7S 
 
 Round Ends 
 
 13330 
 
 12500 
 
 116rt) 
 
 10900 
 
 10140 
 
 9530 
 
 8930 
 
 8370 
 
 7820 
 
 -mi" 
 
 Fixed Ends. . 
 
 13970 
 
 13160 
 
 12400 
 
 11760 
 
 11220 
 
 10690 
 
 10170 
 
 9760 
 
 9270 
 
 -L U n" 
 
 Plat Ends 
 
 139 ;0 
 
 1316012400 
 
 11760 
 
 1 1220 10690J 10170 
 
 9760 
 
 9270 
 
 Heavy.... 
 
 Hinged Ends. . . 
 
 13500 
 
 1261011780 
 
 11110 
 
 10520 9950 
 
 9410 
 
 8960 
 
 8420 
 
 r = 434 
 
 Round Ends 
 
 12830 
 
 11840 
 
 10900 
 
 10140 
 
 9410 8710 
 
 8040 
 
 7530 
 
 6950 
 
 ioy 
 
 Fixed Ends... 
 Flat Ends 
 
 13970 
 13970 
 
 13160 
 
 13160 
 
 12400 
 12400 
 
 11760 
 
 1 1760 
 
 11220(10690 
 1122010690 
 
 10170' 9760 
 10170 9760 
 
 9270 
 9270 
 
 Light .... 
 
 Hinged Ends. . . 
 
 13500 
 
 12610 
 
 117801111010530 
 
 9950 
 
 9410 8960 
 
 8420 
 
 r = 4-2 
 
 Round Ends 
 
 12830 
 
 11840 
 
 109001 10140 
 
 9410 
 
 8710 
 
 8040, 7530 
 
 6950 
 
 1 0" 
 
 Fixed Ends... 
 
 13840 
 
 13030 
 
 1214011490 
 
 10950 
 
 10430 
 
 99L'0 
 
 9430 
 
 8960 
 
 Flat Ends 
 Heavy 1 Hinged Ends. . . 
 
 1384013080 
 
 1335012460 
 
 12 140 11 490 10950! 10430 
 1151010820102301 9680 
 
 9920 9430 
 9140 8600 
 
 8960 
 
 r-s-94 [Round Ends.... 
 
 1267011670 
 
 10600 
 
 9780 
 
 9050 8370 7720 ; 7140 
 
 6580 
 
TABLE OF STRUTS. 
 
 125 
 
 No. 3. 
 PENCOYD I BEAMS AS STRUTS. 
 
 |A 
 
 -C-- 
 
 --D. 
 
 In the marginal columns r indicates the radius of gyration taken around 
 axis A B. When strut is hinged the pins are supposed to lie in the direc- 
 tion A B. Under the conditions stated the strut may be considered flat 
 ended in direction A B. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 OF 
 
 SIZE 
 
 OF 
 
 
 
 
 
 
 
 
 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 42 
 
 ENDS. 
 
 BEAM. 
 
 10600 
 
 10260 
 
 9920 
 
 9510 
 
 9190 
 
 8880 
 
 8580 
 
 8330 
 
 8140 
 
 Fixed Ends... 
 
 1 K" 
 
 10600 
 
 1 02(50 
 
 9920 
 
 9510 9190 
 
 8880 8580 8320 8120 Flat Ends 
 
 10 
 
 9860 
 8600 
 
 9.500 
 815U 
 
 9140 
 
 772U 
 
 8690 
 7240 
 
 8330 
 6S50 
 
 8000 
 6490 
 
 7670 
 6130 
 
 7370 
 5810 
 
 7100 
 5420 
 
 Hinged Ends... 
 Round Ends 
 
 Heavy. 
 
 r== 6-86 
 
 10690 
 
 10340 
 
 10000 
 
 9680 
 
 9350 
 
 9040 
 
 8730 
 
 S420 
 
 8230 
 
 Fixed Ends... 
 
 1 " 
 
 10690 
 
 10340 
 
 10000 
 
 8680 9350 
 
 9040 
 
 8730 
 
 8420 8220 Flat Ends 
 
 10 
 
 9950 
 
 9590 
 
 9230 
 
 8870! 8510 
 
 8160 
 
 7830 
 
 7500; 7240 Hinged Ends. . . 
 
 Light. 
 
 8710 
 
 8260 
 
 7820 
 
 743C 7040 
 
 6670 
 
 6310 
 
 5950 
 
 5660 
 
 Round Ends 
 
 r -= 8-88 
 
 9430 
 
 9040 
 
 8650 
 
 8330, 8090 
 
 7860 
 
 7630 
 
 7410 
 
 7190 
 
 Fixed Ends... 
 
 19" 
 
 9430 
 
 9040 
 
 8650 
 
 8320 1 8070 
 
 7830 i 7590 
 
 7330 
 
 7020 Flat Ends 
 
 L4 
 
 8600 
 7140 
 
 8160 
 6670 
 
 7750 
 6220 
 
 73" 
 5810 
 
 704U 
 5350 
 
 6720 
 5100 
 
 6410 
 4760 
 
 6100 
 4440 
 
 5800 
 4150 
 
 Hinged Ends... 
 Round Ends 
 
 Heavy. 
 
 r = 4-69 
 
 9590 
 
 9190 
 
 8800 
 
 8420 
 
 8180 
 
 7950 
 
 7720 
 
 7500 
 
 7280 
 
 Fixed Ends 
 
 19" 
 
 9590 
 
 9190 
 
 8800 
 
 8420 8170 
 
 7920 7680 
 
 7450; 7140 
 
 Flat Ends... 
 
 1 ~j 
 
 8780 
 
 8830 
 
 7910 
 
 7500 7170 
 
 6840 ; 6530 
 
 6220! 5920 Hinged Ends. . . 
 
 Light. 
 
 7330 
 
 6850 
 
 6400 
 
 5950 
 
 5490 
 
 5230 
 
 4890 
 
 4560 
 
 4270 
 
 Round Ends 
 
 I =4-78 
 
 8800 
 
 8420 
 
 8140 
 
 7860 
 
 7590 
 
 7320 
 
 7070 
 
 6S70 
 
 6620 
 
 Fixed Ends... 
 
 1 ft 1 " 
 
 8800 
 
 8420 
 
 8120 
 
 7830 
 
 7540 7210 6840 
 
 6550 
 
 6210 
 
 Flat Ends 
 
 i-'Vj 
 
 7910 
 
 7500 
 
 7100 
 
 6720 
 
 6340 5980 5620 
 
 5340 
 
 5010 
 
 Hinged Ends... 
 
 Heavy. 
 
 6400 
 
 5950 
 
 5420 
 
 5100 
 
 4690 
 
 4320 
 
 3980 
 
 3710 
 
 3390 
 
 Round Ends 
 
 r = 4-34 
 
 8800 
 
 8420 
 
 8090 
 
 7810 
 
 7540 
 
 7320 
 
 7070 
 
 6870 
 
 6620 
 
 Fixed Ends 
 
 ,, 
 
 8800 
 
 8420 
 
 8070 
 
 7780 
 
 7500 7210! 6840 
 
 6550 
 
 6210 
 
 Flat Ends 
 
 J Uf 
 
 7910 
 
 7500 
 
 7040 
 
 6650 
 
 6280 980 5620 5340 
 
 5010 
 
 Hinged Ends... 
 
 Light. 
 
 6400 
 
 5950 
 
 5350 
 
 5030 
 
 4630 
 
 4320 
 
 3980 
 
 3710 
 
 3390 
 
 Round Ends... . 
 
 r = 4-26 
 
 8500 
 
 8180 
 
 7900 
 
 7630 
 
 7320 
 
 7070 
 
 6830 
 
 6580 
 
 6310 
 
 Fixed Fnds 
 
 1 fj" 
 
 8500 8170 
 
 7870 
 
 7590 
 
 7210 6840 6490J 6160 
 
 5880 
 
 Flat Ends 
 
 1 U 
 
 7580 7170 
 
 6780 
 
 64101 5980 5620 5280 4960 
 
 4670 
 
 Hingc-d Ends... 
 
 Heavy. 
 
 6040 5490 5160 
 
 4760J 4320 3980 3650 3340 
 
 3050 
 
 Round Ends. . . . 
 
 r 3-94 
 
126 WROUGHT IRON AND STEEL. 
 
 No. 4. 
 PENCOYD I BEAMS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 When the struts are secure from failure in the direction of the flanges and 
 can bend only in the direction of the web C D. Using factors of safety 
 given in previous tables. 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OF 
 
 BEAM. 
 
 OP 
 
 ENDS. 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 1 0" 
 
 Fixed Ends 
 
 
 13840 
 
 13030 
 
 12270 
 
 11670 
 
 11130 
 
 10600 
 
 10090 
 
 9590 
 
 1U 
 
 Light . . . 
 
 Flat Ends 
 
 
 13840 
 13350 
 
 13030 12270; 116701 11 130 10600 
 12460I11650H101010420 9860 
 
 10090 
 9320 
 
 9590 
 
 8780 
 
 Hinged Ends 
 
 
 r 4-05 
 
 Round Ends. 
 
 
 12670 
 
 11670 
 
 10750 
 
 10020 9290 
 
 8600 
 
 7930 
 
 7330 
 
 Q" 
 
 Fixed Ends 
 
 14380 
 
 13430 
 
 12650 
 
 11760 
 
 11130 10600 
 
 10000 
 
 9510 
 
 8960 
 
 V 
 
 Flat Ends. ... 
 
 14380 
 
 13430 
 
 12650 11 760! 11 130 
 
 10600 10000 
 
 9510 
 
 8960 
 
 Heavy. . . . 
 
 Hinged Ends. .. 
 
 13940 
 
 12900 
 
 12( 50 11110 10420 
 
 9860 9230 
 
 86fO 
 
 8080 
 
 r = 3-62 
 
 Round Ends 
 
 13330 
 
 12170 
 
 1121010140 
 
 9290 
 
 8600 
 
 7820 
 
 7240 
 
 6580 
 
 Q" 
 
 Fixed Ends.... 
 
 14380 
 
 13570 
 
 1265011890 
 
 11220 
 
 10690 10090 
 
 9590 
 
 9040 
 
 C7 
 
 Flat Ends 
 
 14:380 
 
 13570 
 
 1-2650,1189011220 
 
 10690 1(1090 ! 9590 
 
 9040 
 
 Light .... 
 
 r = 3-66 
 
 Hinged Ends... 
 Round Ends 
 
 13940 
 13330 
 
 13050 
 12330 
 
 12050 
 11210 
 
 11240 
 10290 
 
 10520 
 9410 
 
 9950 
 8710 
 
 9320 
 7930 
 
 8780 
 7330 
 
 8160 
 6670 
 
 Q" 
 
 Fixed Ends... 
 
 14110 
 
 13030 
 
 12140 
 
 11310 
 
 10690 
 
 lOfOO 
 
 9430 
 
 8800 
 
 8330 
 
 o 
 
 Flat Ends 
 
 14110 130301 121401 11310 10690 10000 9430: 8800 
 
 8320 
 
 Heavy 
 
 Hinged Ends... 
 
 13640 
 
 12460 11510 
 
 10620 9950 
 
 9230 86001 7910 
 
 7370 
 
 r =3-21 
 
 Round Ends 
 
 13000 
 
 11670 
 
 10600 
 
 9530 
 
 8710 
 
 7820 
 
 7140 
 
 6400 
 
 5810 
 
 Q" 
 
 Fixed Ends 
 
 14110 13160 
 
 12140 
 
 11400 
 
 10690 
 
 10090 
 
 9510 
 
 8880 
 
 8370 
 
 o 
 
 Flat Ends 
 
 14110 
 
 13160 
 
 12140 
 
 11400 10690 
 
 10(90 1510 88K) 
 
 8370 
 
 Light .... 
 
 Hinged Ends... 
 
 13640 
 
 1261011510 
 
 10720 9950 
 
 9350 
 
 8690 8000 
 
 7430 
 
 r^ 3. us 
 
 Round Ends 
 
 13000 
 
 11840 
 
 10600 
 
 9660 
 
 8710 
 
 7930 
 
 7240 
 
 6490 
 
 5880 
 
 7" 
 
 Fixed Ends 
 
 13570 
 
 12400 
 
 11400 
 
 10690 
 
 9920 
 
 9190 
 
 8500 
 
 8090 
 
 7380 
 
 I 
 
 Flat Ends 113570 
 
 12400 
 
 11400i 10690 
 
 9920 
 
 9190 
 
 8500, 8070 
 
 7640 
 
 Heavy 
 
 Hinged Ends. .. 
 Round Ends 
 
 13050 
 12330 
 
 11780 
 10900 
 
 10720 
 9660 
 
 9950 
 8710 
 
 9140 
 7720 
 
 8380 
 
 6850 
 
 7580 
 6040 
 
 7040 
 5350 
 
 6470 
 4830 
 
 7" 
 
 Fixed Ends 
 
 13700 
 
 12650 
 
 11580 
 
 10860 
 
 10170 
 
 9510 
 
 8800 
 
 8280 
 
 7900 
 
 I 
 
 Flat Ends 
 
 137001265011580 
 
 1086010170 
 
 95101 8800 8270 
 
 7870 
 
 Wtw 
 
 Hinged Ends. .. 
 Round Ends 
 
 1S2WO 12050 10910 
 1250011210 9900 
 
 10130) 9410 8690] 7910 7300 
 8930 8040 7240 6400J 5730 
 
 6780 
 5160 
 
TABLE OF STRUTS. 
 
 127 
 
 No. 4. 
 
 PENCOYD I BEAMS AS STRUTS. 
 U 
 
 -c- 
 
 |B 
 
 In the marginal columns r indicates the radius of gyration taken around 
 axis A B. When strut is hinged the pins are supposed to lie in the direc- 
 tion A B. Under the conditions stated the strut may be considered flat 
 ended iu direction A B. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 SIZE 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 OF 
 
 ENDS. 
 
 OF 
 
 BEAM. 
 
 9110 
 
 81550 
 
 8280 
 
 8000 
 
 7720 
 
 7450 
 
 7190 
 
 6990 
 
 6750 
 
 Fixed Ends... 
 
 10" 
 
 9110 
 
 8650 
 
 8270 7970 
 
 7680 
 
 7390 
 
 7020 
 
 6720 
 
 6370 Flat Ends 
 
 1 \J 
 
 8250 
 
 7750 
 
 7300 
 
 6910 
 
 6530 
 
 6160 
 
 5800 
 
 5500 
 
 5170 Hinged Ends... 
 
 Light. 
 
 6760 
 
 6220 
 
 5730 
 
 5200 
 
 4890 
 
 4500 
 
 4150 
 
 3870 
 
 3540 
 
 Round Ends . . . 
 
 r =4-05 
 
 8420 
 
 8140 
 
 7810 
 
 7540 
 
 7240 
 
 69,50 
 
 6710 
 
 6400 
 
 6090 
 
 Fixed Ends... 
 
 0" 
 
 84-20 
 
 8120 
 
 7780 
 
 7500 7080 
 
 6660 
 
 6310 
 
 5970 
 
 5650 Flat Ends 
 
 V 
 
 7500 
 
 7100 
 
 6650 
 
 6280! 5860 
 
 5450 
 
 5110 
 
 4770 
 
 4440 Hinged Ends.. 
 
 Heavy. 
 
 5950 
 
 5420 
 
 5030 
 
 4630 
 
 4210 
 
 3810 
 
 3490 
 
 3150 
 
 2820 
 
 Round Ends 
 
 i = s-ea 
 
 8580 
 
 8180 
 
 7900 
 
 7590 
 
 7320 
 
 7030 
 
 6790 
 
 6490 
 
 6170 
 
 Fixed Ends... 
 
 Q" 
 
 8580 
 
 8170 
 
 7870! 7540 
 
 7210 6780 
 
 6430 
 
 6070 
 
 5740 Flat Ends... 
 
 t7 
 
 7670 
 
 7170 
 
 6780! 6340 
 
 5980! 5560 
 
 5220 
 
 4860 
 
 4530 Hinged Ends... 
 
 Light. 
 
 6130 
 
 5490 
 
 5160 
 
 4690 
 
 4320 3920 
 
 3600 
 
 3240 
 
 2910 Round Ends.... 
 
 r 3-63 
 
 7950 
 
 7630 
 
 7280 
 
 6990 
 
 6670 6350 
 
 6010 
 
 5710 
 
 5430 
 
 Fixed Ends... 
 
 0" 
 
 7920 
 
 75:iO 
 
 7140 
 
 6?20 6260 5930 
 
 5560 
 
 5230 
 
 4880 Flat Ends... 
 
 o 
 
 6840 
 
 6410 
 
 5920 
 
 5500 
 
 5030 
 
 47'20 
 
 4350 
 
 4010 
 
 3620 Hinged Ends... 
 
 Heavy. 
 
 5230 
 
 4760 
 
 4270 
 
 3870 
 
 3440 
 
 3100 
 
 2730 
 
 2430 
 
 2150 
 
 Round Ends 
 
 r =" 3-21 
 
 8000 
 
 7680 
 
 7320 
 
 7030 
 
 6750 
 
 6400 
 
 6090 
 
 5500 
 
 5510 
 
 Fixed Ends... 
 
 Q" 
 
 7970 
 
 7640 7210' 6730 
 
 6370 
 
 5970 
 
 5650 
 
 5340 4<)80Flat Ends 
 
 O 
 
 6910 
 
 64701 5980 5560 
 
 5170 
 
 4770 
 
 4440 4120 
 
 3730 Hinged Ends... 
 
 Light. 
 
 5200 
 
 4830 
 
 4320 
 
 3921) 
 
 3540 
 
 3150 
 
 2820 
 
 2510 
 
 2230 1 Round Ends.... 
 
 r =3-25 
 
 7280 
 
 6950 
 
 6580 
 
 6110 
 
 5800 
 
 5470 
 
 5110 
 
 4740 
 
 4370: Fixed Ends... 
 
 hn 
 
 7110 
 
 6660 
 
 6160 5740' 5340: 4930 
 
 4490 
 
 4090 
 
 3710 Flat Ends 
 
 ( 
 
 5920 
 
 54,50 
 
 4960 4530 4120! 3680 
 
 3210 
 
 2800 
 
 2440 Hi used Ends... 
 
 Heavy. 
 
 4270 
 
 3810 
 
 3340 
 
 2910 
 
 2510 
 
 2190 
 
 1860 
 
 1620 
 
 1420 
 
 Round Ends 
 
 I = 2-75 
 
 7500 
 
 7150 
 
 6830 
 
 6440 
 
 6090 
 
 5750 
 
 5430 
 
 5070 
 
 4740 
 
 Fixed Ends . . . 
 
 H" 
 
 7450 
 
 (5960 
 
 6490 6020 5650 
 
 5280 
 
 48SO 
 
 4440 
 
 4090: Flat, Ends 
 
 I 
 
 6220 
 4560 
 
 5740 
 4090 
 
 5280 4820 ! 4440 
 3650 3200 2820 
 
 4060 
 2470 
 
 362o 
 2150 
 
 3160 
 1830 
 
 280i (Hinged Ends... 
 1620 Round Ends. . . 
 
 r Ljght. 9 
 
128 TABLES OF STRUTS. 
 
 No. 5. 
 
 PENCOYD I BEAMS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PEE SQUARE INCH OF SECTION. 
 
 When the struts are secure from failure in the direction of the flanges, and. 
 can bend only in the direction of the web C. D. Using factors of safety 
 given in previous tables. 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OP 
 
 BKAM 
 
 OP 
 TT-wTia 
 
 
 
 
 
 
 
 
 
 
 
 JjjNDS. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 6" 
 
 Fixed Ends 
 
 
 14240 
 
 12900 
 
 11 580 
 
 10690 
 
 9840 
 
 8960 
 
 S9sn 
 
 7810 
 
 
 Flat Ends 
 
 
 14240 
 
 12900 '11580 
 
 10690 9840 
 
 8960 8270 
 
 7780 
 
 Heavy 
 
 r = 2-31 
 
 Hinged Ends... 
 Round Ends 
 
 
 
 13790 
 13160 
 
 1232010910 
 11520J 9900 
 
 9950 
 8710 
 
 9050 
 7630 
 
 8080 
 6580 
 
 7300 
 5730 
 
 6650 
 5030 
 
 6" 
 
 Fixed Ends 
 
 
 14380 
 
 13030 
 
 mfio 
 
 10050 
 
 10090 
 
 9270 
 
 8KOO 
 
 8000 
 
 
 Flat Ends 
 
 
 1 WS;t 
 
 13030 11760 \ 10950 10090 
 
 9270 8500 
 
 7970 
 
 Light. . . 
 
 Hinged Ends 
 
 113340 
 
 12460 11110 10230 1 93-20 
 
 8420 7580 
 
 6910 
 
 I =- 2-4S 
 
 Round Ends. . . . 
 
 
 13330 
 
 11670 
 
 10140 
 
 9050 
 
 7930 
 
 6950 6040 
 
 5200 
 
 5" 
 
 Fixed Ends 
 
 
 13840 
 
 13840 
 
 12270 
 12270 
 
 1104010000 
 1104010000 
 
 9040 
 9040 
 
 8230 7680 
 8220; 7640 
 
 7110 
 
 6900 
 
 Flat Ends... 
 
 __ 
 
 Heavy 'Hin<rpri TCnrls 
 
 
 133:>i> 
 
 11650 
 
 10330 9230 8160 
 
 7240 6470 
 
 5680 
 
 r = 1 
 
 Round Ends 
 
 
 12670 
 
 10750 
 
 9170 
 
 7820 6670 
 
 5660 4830 
 
 4030 
 
 K" 
 
 Fixed Ends.... 
 
 
 14110 
 
 12650 
 
 11400 
 
 10340 9430 
 
 8580 1 8000 
 
 7500 
 
 J 
 
 Flat Ends 
 
 
 14110 
 
 12650 
 
 1140010340 9430 
 
 8580 7970 
 
 7450 
 
 Li ff ht 
 
 Hinged Ends 
 
 
 13640 
 
 12050 10720' 95901 Km 
 
 7670 MI in 
 
 6220 
 
 r = 2-0 
 
 Round Ends . . . 
 
 
 1300011210 
 
 9660 
 
 8260 
 
 7140 
 
 6130 
 
 5200 
 
 4560 
 
 
 
 
 | 
 
 
 
 
 
 
 
 4" 
 
 Fixed Ends 
 
 
 1316011400 
 13160 11400 
 
 10090 
 10090 
 
 8880 
 8880 
 
 8040 
 
 8020 
 
 7370 
 
 7270 
 
 6750 
 6370 
 
 6130 
 5700 
 
 Flat Ends 
 
 
 Heavy 
 
 Hinged Ends.. 
 
 
 12610 10720 
 
 9320 8000 
 
 6970 
 
 6040 
 
 5170 
 
 4480 
 
 r = 1-63 
 
 Round Ends. . 
 
 
 11840 9660 
 
 7930 
 
 6490 
 
 5270 
 
 4380 
 
 3540 
 
 2870 
 
 
 
 A" 
 
 Fixed Ends... 
 
 
 13160 11400 
 
 10170 
 
 8960 
 
 8090 
 
 7410 
 
 6830 
 
 6170 
 
 T: 
 
 Flat Ends 
 
 
 1316011400 
 
 10170 8960 
 
 8070 7330 
 
 6490 
 
 5740 
 
 Light. . . 
 
 Hinged Ends 
 
 12610 10720 
 
 9410i 8080 
 
 7040! 6100 
 
 5280 
 
 4530 
 
 r = 1-63 
 
 Round Ends 
 
 
 11840 
 
 9660 
 
 8040 
 
 6580 
 
 5350 
 
 4440 
 
 3650 
 
 2910 
 
 0" 
 
 Fixed Ends... 
 
 1438ol 11760 
 
 10000 
 
 8500 
 
 7540 
 
 6710 
 
 5840 
 
 5030 
 
 4210 
 
 o 
 
 Flat Ends j 143801 1 1760 10000 
 
 8500 7500 
 
 6310 
 
 5380 
 
 4390 
 
 3540 
 
 Heavy. . . . 
 
 Hinged Ends. . . \ 13940 11110 9230 
 
 7580 6280 
 
 5110 
 
 4160J 3110 
 
 2280 
 
 r =1-21 
 
 Round Ends 
 
 13330 
 
 10140 
 
 7820 
 
 6040 
 
 4630 
 
 3490 
 
 2550 
 
 1790 
 
 1330 
 
 0" 
 
 Fixed Ends 
 
 14520 
 
 12010 
 
 10170 
 
 8650 
 
 7680 
 
 6870 6050 
 
 5230 
 
 4450 
 
 o 
 
 Light 
 
 Flat Ends 
 Hinged Ends... 
 
 14520 12010 10170 
 14090 11380 9410 
 
 8650 7640 
 7750 6470 
 
 6550 5610 4630 
 5340 4390| 3360 
 
 3790 
 2520 
 
 * = 1-26 
 
 Round Ends 
 
 13500 
 
 10440, 8040 
 
 6220 4830 
 
 3710 
 
 2780 
 
 1970 
 
 1460 
 
TABLES OP STKUTS. 
 
 No. 5. 
 PENCOYD I BEAMS AS STRUTS. 
 
 |A 
 I 
 
 129 
 
 LB 
 
 In the marginal columns r indicates the radius of gyration taken around 
 axis A. B. When strut is hinged the pins are supposed to lie in the direc- 
 tion A. B. Under the conditions stated the strut may be considered flat 
 ended in direction A. B. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 SIZE 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 30 
 
 32 
 
 34 
 
 36 
 
 OF 
 
 ENDS. 
 
 OP 
 
 BEAM. 
 
 7320 
 
 6910 
 
 6440 
 
 C010 
 
 5590 5150 
 
 4740 4290 
 
 3930 
 
 Fixed Ends... 
 
 
 7210 
 
 6600 
 
 (5020 
 
 5560 
 
 5080 4540 
 
 4090 3620 
 
 3280 Flat Ends 
 
 O 
 
 5980 
 
 5390 
 
 4820 
 
 4350 
 
 3840 3260 
 
 2800 23(50 
 
 2080 Hinged Ends... 
 
 Heavy. 
 
 4320 
 
 3760 
 
 3200 
 
 2730 
 
 2310 
 
 1900 
 
 1620 1370 
 
 1190 
 
 Round Ends . . . 
 
 r = 2-31 
 
 7540 
 
 7110 
 
 6710 
 
 6310 
 
 5880 
 
 5470 
 
 5070 4650 
 
 4250 Fixed Ends... 
 
 a" 
 
 7500 
 
 6900 
 
 6310 
 
 5880 
 
 5430 
 
 4930 4440 4000 
 
 3580 Flat Ends 
 
 O 
 
 6280 
 
 5680 
 
 5110 
 
 4670 
 
 4210 
 
 3680 3160 2720 
 
 2320 Hintred Ends... 
 
 Light. 
 
 4630 
 
 4030 
 
 3490 
 
 3050 
 
 2600 
 
 2190 1830 1570 
 
 1350 
 
 Round Ends 
 
 r 2-43 
 
 6620 
 
 6090 
 
 5590 
 
 5110 
 
 4610 
 
 4130 3730 3340 
 
 2970 
 
 Fixed Ends... 
 
 5" 
 
 6210 
 
 5650 
 
 5080 
 
 4490 
 
 3960 
 
 3460 3100 2780 
 
 2500 Flat Ends 
 
 ' 
 
 5010 
 3390 
 
 4440 
 
 2820 
 
 3840 
 2310 
 
 3210 
 1860 
 
 2680 2220 
 1550 1290 
 
 1950 
 1100 
 
 1690 
 940 
 
 1450 
 820 
 
 Hinged Ends... 
 Round Ends 
 
 Heavy. 
 
 r =- 1-99 
 
 7030 
 
 6580 
 
 6090 
 
 5630 
 
 51501 4090 
 
 4250 3860 
 
 3500 
 
 Fixed Ends.... 
 
 5" 
 
 6780 
 
 6160 
 
 5650 
 
 5130 
 
 4540 
 
 4040 
 
 3580 3220 
 
 2900 
 
 Flat Ends 
 
 
 5560 
 3920 
 
 4960 
 3340 
 
 4440 
 
 2820 
 
 3900 
 2350 
 
 3260 
 1900 
 
 2760 
 1590 
 
 2320 2040 
 1350 1160 
 
 1800 
 1000 
 
 Hinged Ends... 
 Round Ends 
 
 Light. 
 
 r =2-08 
 
 5510 4910 
 
 4290 
 
 3790 
 
 3310 
 
 2850 
 
 2500 2180 
 
 1900 
 
 Fixed Ends 
 
 A" 
 
 4980 | 4260 
 
 3620 3160 
 
 2760 
 
 2420 
 
 2140 1910 
 
 1680 
 
 Flat Ends 
 
 
 
 3730! 2970 
 
 2360 1990 
 
 1670 
 
 1380 
 
 1180 
 
 1040 
 
 900 
 
 Hinged Ends... 
 
 Heavy. 
 
 2230 
 
 1710 
 
 1370 
 
 1130 
 
 930 
 
 780 
 
 670 
 
 600 
 
 520 
 
 Round Eiids. . . . 
 
 r = 1-63 
 
 5590 
 
 5000 
 
 4410 
 
 3860 
 
 3400 
 
 2940 
 
 2570 
 
 2240 
 
 1930 
 
 Fixed Ends 
 
 4t f 
 
 5080 4350 
 
 3750 3220 
 
 2830 
 
 2480 
 
 2190 
 
 1950 
 
 1720 
 
 Flat Ends 
 
 
 3840 3060 
 
 2480 2040 
 
 1730 
 
 1430 
 
 1220 
 
 1070 
 
 920 
 
 Hinged Ends... 
 
 Light. 
 
 2310 1760 
 
 1440 
 
 1160 
 
 960 
 
 810 
 
 690 
 
 610 
 
 540 
 
 Round Ends 
 
 r =1.65 
 
 3560 2940 
 
 2450 
 
 2000 
 
 1740 
 
 1520 
 
 1320 
 
 1120 
 
 990 
 
 Fixed Ends... 
 
 0" 
 
 2950 2480 
 
 2100 1780 
 
 1490 1220 
 
 1000 
 
 820 
 
 670 Flat Ends 
 
 o 
 
 1840 
 1030 
 
 1430 
 
 810 
 
 1160 
 660 
 
 960 
 560 
 
 800 680 
 450 370 
 
 590 
 320 
 
 500 
 260 
 
 420 Hinged Ends... 
 230 Round Ends 
 
 Heavy. 
 
 r = 1-21 
 
 3760 
 
 3150 
 
 2R10 
 
 2180 
 
 1850 
 
 1630 
 
 1420 
 
 1220 
 
 1060 
 
 Fixed Ends... 
 
 0" 
 
 3130 
 
 2640 
 
 2230; 1910 
 
 1620 
 
 1350 1110 900 
 
 750 Flat Ends 
 
 O 
 
 1970 
 
 1570 
 
 1240 1040 
 
 870 
 
 740 
 
 630 ; 550 
 
 460 Hinged Ends... 
 
 Lieht. 
 
 1120 
 
 880 
 
 710 600 
 
 500 
 
 410 
 
 350 290 
 
 240|Round Ends 
 
 r = 1-26 
 
130 TABLES OF STEUTS. 
 
 No 6. 
 PENCOYD I BEAMS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 When the struts are free to bend at right angles to the web ; or in the 
 weakest direction C. D. Using factors of safety given in previous tables. 
 
 SIZE 
 
 OP 
 
 BEAM. 
 
 CONDITION 
 
 OP 
 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 15" 
 
 Fixed Ends.... 
 
 14380 
 
 11760 
 
 10000 
 
 8420 
 
 7500 
 
 6670 
 
 5800 
 
 5000 
 
 4170 
 
 -L V 
 
 Flat Ends 
 
 14380 11760 
 
 10000 
 
 8420 
 
 7450 
 
 6260 
 
 5340 
 
 4350 
 
 3500 
 
 Heavy 
 
 r= 1-20 
 
 Hinged Ends... 
 Round Ends 
 
 13940111110 
 1333010140 
 
 9230 
 
 7820 
 
 7500 
 5950 
 
 6220 
 4560 
 
 5G60 
 3440 
 
 4120 
 2510 
 
 306! 
 1760 
 
 2250 
 1310 
 
 1 V 
 
 Fixed Ends 
 
 1411011400 
 
 9439 
 
 8000 
 
 7030 
 
 6090 
 
 5150 
 
 4250 
 
 3500 
 
 J. *J 
 
 Light 
 
 Flat Ends 
 Hinged Ends... 
 
 1411011409 
 13640 10720 
 
 9433 
 8630 
 
 7970 
 6910 
 
 6780 
 5560 
 
 5650 
 4440 
 
 4540 
 3260 
 
 358( 
 
 2323 
 
 2900 
 1800 
 
 r= 1-08 
 
 Round Ends 
 
 13000 
 
 9660 
 
 7140 
 
 5200 
 
 3920 
 
 2820 
 
 1900 
 
 1350 
 
 1000 
 
 10" 
 
 Fixed Ends... 
 
 14240 
 
 11670 
 
 9840 
 
 8330 
 
 7370 
 
 6530 
 
 5630 
 
 4820 
 
 4000 
 
 &.! 
 
 Flat Ends 
 
 14240 
 
 11670 
 
 9840 
 
 8320 
 
 7270 
 
 6110 
 
 5130 
 
 4170 
 
 3340 
 
 Heavy 
 
 Hinged Ends.. . 
 
 13790 
 
 11010 
 
 9059 
 
 7370 
 
 6040 
 
 4910 
 
 3900 
 
 2890 
 
 2130 
 
 r = 1-17 
 
 Round Ends 
 
 13160 
 
 10020 
 
 7630 
 
 5810 
 
 4380 
 
 3290 
 
 2350 
 
 1660 
 
 1230 
 
 10" 
 
 Fixed Ends... 
 
 13840 
 
 11040 
 
 9110 
 
 7720 
 
 6710 
 
 5670 
 
 4740 
 
 3830 
 
 3060 
 
 I 
 
 Flat Ends 
 
 13840 
 
 11049 
 
 9110 
 
 7680 
 
 6310 
 
 5180 
 
 4090 
 
 3190 
 
 2570 
 
 Light .... 
 
 Hinged Ends. .. 
 
 13350 
 
 10339 
 
 8250 
 
 6530 
 
 5110 
 
 39501 2800 
 
 2020 
 
 1510 
 
 r = 1-01 
 
 Round Ends 
 
 12670 
 
 9170 
 
 6760 
 
 4890 
 
 3490 
 
 2390 
 
 1620 
 
 1150 
 
 850 
 
 10-i" 
 
 Fixed Ends 
 Plat Ends 
 
 14380 
 143 
 
 11760 
 
 1176C 
 
 10000 
 100CO 
 
 8370 
 
 8370 
 
 7450 
 7390 
 
 6620 
 6210 
 
 57HO 
 
 5280 
 
 4950 
 4300 
 
 4130 
 3460 
 
 Heavy, . . . 
 
 Hinged Ends... 
 
 13910 
 
 11110 
 
 9230 
 
 7439 
 
 6160 
 
 5010 
 
 4060; 3010 
 
 2220 
 
 r = 1-19 
 
 Round Ends 
 
 13330 
 
 10140 
 
 7820 
 
 5880 
 
 4500 
 
 3390 
 
 2470 
 
 1730 
 
 1290 
 
 10 1 " 
 
 Fixed Ends 
 
 13840 
 
 10950 
 
 8960 
 
 7590 
 
 6580 
 
 5510 
 
 4530 
 
 3630 
 
 2880 
 
 
 Flat Ends 
 
 13840 10950 
 
 8960 
 
 7540 
 
 6160 
 
 4989 
 
 3870 
 
 3010 
 
 2440 
 
 Light 
 
 Hinged Ends... 
 
 1335010230 8080 6340 
 
 4960 
 
 37:30 
 
 8600 
 
 1880 
 
 1400 
 
 r = 87 
 
 Round Ends 
 
 12670 9050 
 
 | 
 
 6580 
 
 4690 
 
 3340 
 
 2230 
 
 1500 
 
 1060 
 
 790 
 
 10" 
 
 Fixed Ends ... 
 
 13S4o' 10950 
 
 8960 
 
 7590 
 
 6580 
 
 5510 
 
 4530 
 
 3630 
 
 2880 
 
 L\J 
 
 Flat Ends 
 
 1384010950 8960 
 
 7540 
 
 6160 4980 
 
 3870 
 
 3010 
 
 2440 
 
 Heavy. . . 
 
 Ringed Ends . . . 
 
 1*350 10230 
 
 80SO 
 
 6340 
 
 49601 3730 
 
 2600 
 
 1880 
 
 1400 
 
 I = -98 
 
 Round Ends 
 
 12670 9050 
 
 6580 
 
 4690 
 
 33401 2230 
 
 1500 
 
 1060 
 
 790 
 
 
 
 
 
 
 
 I 
 
 
 
 
TABLES Or STRUTS. 
 
 3 31 
 
 No. 6. 
 PENCOYD I BEAMS AS STRUTS. 
 
 L 
 
 !" 
 
 In the marginal columns r indicates the radius of gyration taken around 
 axis A. B. When the strut is hinged the pins are supposed to lie in the di- 
 rection A. B. If the pins lie in the direction C. D. consider the strut flat 
 ended by this table. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 SIZE 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 OF 
 
 ENDS. 
 
 OP 
 
 BEAM. 
 
 3500 
 
 2880 
 
 2410 
 
 1960 
 
 1720 
 
 1500 
 
 1290 
 
 1090 
 
 980 
 
 Fixed Ends... 
 
 15" 
 
 2900 
 
 2440 
 
 2070 
 
 1750 
 
 1460 
 
 1200 
 
 970 
 
 800 
 
 650 Flat Ends 
 
 10 
 
 1800 
 1000 
 
 1400 
 790 
 
 1140 
 650 
 
 940 
 550 
 
 790 
 
 440 
 
 670 
 370 
 
 580 
 320 
 
 490 
 260 
 
 420 
 230 
 
 Hinged Ends... 
 Round Ends 
 
 Heavy. 
 
 r = 1-20 
 
 2830 
 2400 
 
 2310 
 
 2000 
 
 1870 
 1650 
 
 1620 
 1340 
 
 1380 
 1060 
 
 1160 
 820 
 
 1000 
 670 
 
 860 
 520 
 
 740 
 430 
 
 Fixed Ends 
 Flat Ends 
 
 15" 
 
 1370 
 
 1100 
 
 890 
 
 730 
 
 610 
 
 520 
 
 430 
 
 340 
 
 280 
 
 Hinged Ends... 
 
 Light. 
 
 770 
 
 630 
 
 510 
 
 410 
 
 340 
 
 280 
 
 230 
 
 200 
 
 170 
 
 Round Ends. . . . 
 
 r = 1-08 
 
 &340 
 
 2780 
 
 2730 
 2320 
 
 2270 
 1970 
 
 1870 
 1650 
 
 1640 
 1360 
 
 1410 
 1100 
 
 1210 
 
 890 
 
 1040 
 
 720 
 
 920 
 
 580 
 
 Fixed Ends 
 Flat Ends... 
 
 12" 
 
 1690 
 
 1310 
 
 1080 
 
 890 
 
 740 
 
 630 
 
 540 
 
 450 
 
 380 Hinged Ends... 
 
 Heavy. 
 
 940 
 
 740 
 
 620 
 
 510 
 
 410 
 
 350 
 
 290 
 
 240 
 
 210 
 
 Round Ends 
 
 r = I'll 
 
 450 
 
 1940 
 
 1660 
 
 1400 
 
 1160 
 
 1000 
 
 850 
 
 720 
 
 
 Fixed Ends.... 
 
 10" 
 
 2100 
 
 1730 
 
 1390 
 
 1090 
 
 850 
 
 670 
 
 510 
 
 410 
 
 
 Flat Ends 
 
 JL -i 
 
 1160 
 
 930 
 
 760 
 
 620 
 
 520 
 
 430 
 
 340 
 
 270 
 
 
 
 Hinged Ends... 
 
 Light. 
 
 660 
 
 540 
 
 420 
 
 350 
 
 280 
 
 230 
 
 200 
 
 160 
 
 
 Round Ends 
 
 r = 1-01 
 
 3430 
 
 2830 
 
 2360 
 
 1930 
 
 1690 
 
 1470 
 
 1260 
 
 1070 
 
 960 
 
 Fixed Ends 
 
 10 1 " 
 
 2850 
 1750 
 970 
 
 2400 
 1370 
 770 
 
 2d30 
 1120 
 640 
 
 1720 
 920 
 540 
 
 1430 
 770 
 430 
 
 1170 
 660 
 360 
 
 940 
 560 
 310 
 
 770 
 470 
 250 
 
 620 
 400 
 220 
 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Heavy. 
 
 r= I-M 
 
 2290 
 
 1850 
 
 1560 
 
 1310 
 
 1070 
 
 930 
 
 780 
 
 670 
 
 
 Fixed Ends 
 
 i n i " 
 
 1990 
 
 1620 
 
 1270 
 
 990 
 
 770 
 
 600 
 
 460 
 
 380 
 
 
 Flat Ends . . . 
 
 lU^r 
 
 1090 
 
 870 
 
 700 
 
 580 
 
 470 
 
 390 
 
 300 
 
 240 
 
 
 HingedEnds... 
 
 r L -^?7 
 
 620 
 
 500 
 
 390 
 
 320 
 
 250 
 
 210 
 
 170 
 
 150 
 
 
 Round Ends. . . . 
 
 
 2290 
 
 1850 
 
 1560 
 
 1310 
 
 1070 
 
 930 
 
 780 
 
 670 
 
 
 Fixed Ends... 
 
 1 f\tt 
 
 1990 
 
 1620 
 
 1270 
 
 990 
 
 770 
 
 600 
 
 460 
 
 380 
 
 '.'. Flat Ends 
 
 JL W 
 
 1090 
 620 
 
 870 
 500 
 
 700 
 390 
 
 580 
 320 
 
 470 
 250 
 
 390 
 210 
 
 300 
 170 
 
 240 
 150 
 
 
 
 Hinged Ends... 
 Round Ends.... 
 
 Heavy. 
 
 r = -98 
 
132 TABLES OF STKUTS. 
 
 No. 7. 
 PENCOYD I BEAMS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 The strut is supposed to be free to bend in the weakest direction C. D. 
 The radius of gyration is taken around A. B. 
 
 SIZE 
 
 OK 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 BEAM. 
 
 OF 
 
 ENDS. 
 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 10" 
 
 Fixed Ends... 
 Flat Ends 
 
 1370010770 
 13700 10770 
 
 8730 
 8730 
 
 7450 
 7390 
 
 6400 
 5970 
 
 5310 
 
 4730 
 
 4290 
 3620 
 
 3430 
 
 2850 
 
 2710 
 2300 
 
 Liirht . . 
 
 r "= -95 
 
 Hinged Ends... 
 Round Ends 
 
 13200 
 12500 
 
 10040 
 , 8820 
 
 7839 
 6310 
 
 61(50 
 4500 
 
 4770 
 3150 
 
 3460 
 2040 
 
 1 2360 
 1370 
 
 1750 
 970 
 
 1300 
 740 
 
 9" 
 
 Fixed Ends 
 
 13700 
 
 10860 
 
 8800 
 
 7500 
 
 6440 
 
 5390 
 
 4370 
 
 3500 
 
 2760 
 
 t/ 
 
 Flat Ends 
 
 137001 10860 
 
 8800 
 
 7450 
 
 6020 
 
 4830 
 
 3710 
 
 2900 
 
 2340 
 
 Heavy 
 
 Elinged Ends. .. 
 
 13200 
 
 10130 
 
 7910 
 
 6220 
 
 4820 
 
 3570 
 
 2440 
 
 1800 
 
 1330 
 
 r = -98 
 
 Round Ends 
 
 12500 
 
 8930 
 
 6400 
 
 4560 
 
 3200 
 
 2120 
 
 1420 
 
 1000 
 
 750 
 
 9" 
 
 Fixed Ends.... 
 
 13430 
 
 10520 
 
 8370 
 
 7150 
 
 6010 
 
 4910 
 
 3860 
 
 3000 
 
 2340 
 
 u 
 
 Flat Ends 
 
 13430 
 
 10520 
 
 8370 
 
 6960 
 
 5560 
 
 4260 
 
 3220 
 
 2530 
 
 2020 
 
 Light 
 
 iinged Ends... 
 
 12900 
 
 9770 
 
 7430 
 
 5740 
 
 4350 
 
 2970 
 
 2040 
 
 1470 1110 
 
 r = -89 
 
 Round Ends 
 
 12170 
 
 8490 
 
 5880 
 
 4090 
 
 2730 
 
 1710 
 
 1160 
 
 830 630 
 
 C" 
 
 r^ixed Ends 
 
 13."70 
 
 10770 
 
 8650 
 
 7410 
 
 6310 
 
 5270 
 
 4210 
 
 3370 i 2640 
 
 o 
 
 ?lat Ends 
 
 l.:57) 10770 
 
 8659 
 
 7339 
 
 5880 
 
 4680 
 
 3540 2800! 2250 
 
 Heavy 
 
 ttngedEnds... 
 
 1305J 
 
 10040 
 
 7750 
 
 6100 
 
 4670 
 
 3410 
 
 2280 
 
 17101 1260 
 
 r = ! 
 
 Sound Ends 
 
 12330 
 
 8820 
 
 6220 
 
 4440 
 
 3050 
 
 2010 
 
 1330 
 
 950 
 
 720 
 
 C" 
 
 Fixed Ends... 
 
 3430 
 
 10430 
 
 8330 
 
 7110 
 
 5960 
 
 4820 
 
 3790 
 
 2940 
 
 2290 
 
 o 
 
 Hut Ends 
 
 3439 
 
 10430 
 
 8320 
 
 6900 
 
 5520 
 
 4170 
 
 3160 
 
 2480! 1990 
 
 Light 
 
 linged Ends... 
 
 9900 
 
 9680 
 
 7370 
 
 5680 
 
 4300 
 
 2899 
 
 1990 
 
 1430 1090 
 
 r '68 
 
 Round Ends 
 
 2170 
 
 8370 
 
 5810 
 
 4030 
 
 2690 
 
 1660 
 
 1130 
 
 810 
 
 620 
 
 Hit 
 
 <Mxed Ends 
 
 3930 
 
 99 ?0 
 
 7990 
 
 6620 
 
 5310 
 
 4100 
 
 3990 
 
 2340 
 
 1800 
 
 t 
 
 Hat Ends 
 
 :5 i:jo 
 
 9920 
 
 7870 
 
 6210 
 
 4730 
 
 3430 
 
 2600 
 
 2020 1560 
 
 Heavy 
 
 lingedEnds... 
 
 2460 
 
 9140 
 
 6780 
 
 5010 
 
 3469 
 
 2200 
 
 1530 
 
 1110 840 
 
 r = -79 
 
 lound Ends 
 
 1670 
 
 7720 
 
 5160 
 
 3390 
 
 2040 
 
 1270 
 
 860 
 
 630J 480 
 
 Hit 
 
 Fixed Ends.... 
 
 3160 
 
 10090 
 
 8040 
 
 6790 
 
 5550 
 
 4330 
 
 3340 
 
 2540 1920 
 
 I 
 
 Flat Ends 
 
 3160 
 
 10090 
 
 8020 
 
 6430 
 
 5039 
 
 360 
 
 2780 
 
 2170' 1700 
 
 Light. . . . 
 
 fringed Ends... 
 
 2610 
 
 9320 
 
 6H70 
 
 5220 
 
 3790 
 
 2400 
 
 1690 
 
 1210 910 
 
 r = -82 
 
 Round Ends 
 
 1840 
 
 7930 
 
 5270 
 
 3600 
 
 2270 
 
 1390 
 
 940 
 
 690 
 
 530 
 
TABLES OF STBUTS. 
 
 133 
 
 No. 7. 
 PENCOYD I BEAMS AS STRUTS. 
 
 A. B. indicates the direction of pins for hinged struts in this table. If the 
 pins are placed in the direction 6'. D. consider the strut as flat ended, r in 
 marginal columns inclica es radius of gyration around A. B. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 OF 
 
 ENDS. 
 
 SIZE 
 
 OP 
 
 BEAM. 
 
 20 
 
 2110 
 
 I860 
 1010 
 580 
 
 2180 
 1910 
 1040 
 
 600 
 
 1840 
 1610 
 
 870 
 500 
 
 2070 
 1830 
 990 
 570 
 
 1800 
 1560 
 840 
 480 
 
 1450 
 1150 
 650 
 3GO 
 
 1570 
 1290 
 710 
 390 
 
 22 
 
 24 
 
 1460 
 1160 
 650 
 360 
 
 1500 
 1200 
 670 
 370 
 
 1250 
 930 
 560 
 300 
 
 1430 
 1120 
 K40 
 350 
 
 1220 
 900 
 550 
 290 
 
 950 
 610 
 400 
 
 220 
 
 1030 
 710 
 440 
 230 
 
 26 
 
 28 
 
 30 
 
 850 
 510 
 340 
 200 
 
 880 
 540 
 360 
 200 
 
 720 
 410 
 270 
 160 
 
 830 
 490 
 330 
 190 
 
 700 
 400 
 250 
 160 
 
 32 
 
 34 
 
 36 
 
 1740 
 1490 
 800 
 450 
 
 1780 
 1530 
 S30 
 470 
 
 1530 
 1230 
 680 
 380 
 
 1700 
 1440 
 780 
 430 
 
 1500 
 1200 
 67'0 
 370 
 
 1150 
 840 
 20 
 270 
 
 1270 
 950 
 570 
 310 
 
 1210 
 890 
 540 
 290 
 
 1240 
 920 
 560 
 300 
 
 1030 
 710 
 440 
 230 
 
 1170 
 860 
 530 
 280 
 
 1010 
 680 
 430 
 230 
 
 770 
 450 
 290 
 170 
 
 850 
 510 
 340 
 200 
 
 1020 
 690 
 440 
 230 
 
 1040 
 720 
 450 
 240 
 
 860 
 520 
 340 
 200 
 
 990 
 670 
 
 420 
 230 
 
 840 
 500 
 330 
 190 
 
 720 
 410 
 270 
 160 
 
 740 
 430 
 280 
 170 
 
 
 
 
 
 Fixed Ends 
 Flat Ends 
 Hinged inds... 
 Round Ends 
 
 Fixed Ends... 
 Flat Ends . 
 
 10" 
 
 , L I**i 
 
 9" 
 
 Heavy. 
 
 r ==' -9 
 
 9" 
 
 Light. 
 
 r = -89 
 
 8" 
 
 Heavy. 
 
 8" 
 , L '.-, 
 
 1" 
 
 Heavy. 
 
 r = -79 
 
 r 
 ,w.i 
 
 
 
 
 
 
 
 
 
 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinjred Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends.... 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 
 
 
 
 
 
 
 
 
 
 700 
 400 
 250 
 160 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 700 
 400 
 250 
 1HO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
134 TABLES OF STRUTS. 
 
 No. 8. 
 PENCOYD I BEAMS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 (See remarks at head of Tables No. 6 and 7.) 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OK 
 
 BEAM 
 
 OP 
 
 ENDS. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 fi" 
 
 Fixed Ends 
 
 12140 
 
 8880 
 
 7030 5470 
 
 4000 
 
 2830 
 
 2000 
 
 1550 
 
 1170 
 
 O 
 
 Flat Ends 
 
 12140 
 
 8880 
 
 6780 4930 
 
 3340 
 
 2400 
 
 1180 
 
 1260 
 
 860 
 
 Heavy 
 
 Hinged Ends... 
 
 11510 
 
 8000 
 
 5560 3680 
 
 2130 
 
 1370 
 
 960 
 
 700 
 
 530 
 
 r = -65 
 
 Round Ends 
 
 10600 
 
 6490 
 
 3920 
 
 2190 
 
 12,0 
 
 770 
 
 560 
 
 390 
 
 2SO 
 
 a" 
 
 Fixed Ends 
 
 12270 
 
 8960 
 
 7110 
 
 5590 
 
 4100 
 
 2940 
 
 2090 
 
 1590 
 
 1220 
 
 o 
 
 Flat Ends 
 
 12270 
 
 8960 
 
 6900 5080 
 
 3430 
 
 2480 
 
 1840 
 
 1310 
 
 900 
 
 Light .... 
 
 Hinged Ends... 
 
 11650 
 
 8080 
 
 5680 3840 
 
 2200 
 
 1430 
 
 1000 
 
 720 
 
 550 
 
 r =- -68 
 
 Round Ends 
 
 10750 
 
 6580 
 
 4030 
 
 2310 
 
 1270 
 
 810 
 
 580 
 
 400 
 
 290 
 
 K" 
 
 Fixed Ends.... 
 
 11760 
 
 8420 
 
 66701 5000 
 
 3500 
 
 2410 
 
 1720 
 
 1290 
 
 980 
 
 u 
 
 Flat Ends 
 
 11760 
 
 8420 
 
 6260 
 
 43501 2900 
 
 2070 
 
 1460 
 
 970 
 
 650 
 
 Heavy 
 
 Hinged Ends... 
 
 11110 
 
 7500 
 
 50CO 
 
 30601 1800 
 
 1140 
 
 790 
 
 580 
 
 420 
 
 r = -60 
 
 Round Ends 
 
 10140 
 
 5950 
 
 3440 
 
 1760 
 
 1000 
 
 650 
 
 440 
 
 320 
 
 230 
 
 K" 
 
 Fixed Ends.... 
 
 11760 
 
 8420 
 
 6670 
 
 5000 
 
 3500 
 
 2410 
 
 1720 
 
 1290 
 
 980 
 
 t_J 
 
 Flat Ends 
 
 11760 
 
 8420 
 
 6260 
 
 4350 ! 2900 
 
 207'0 
 
 1460 
 
 970 
 
 650 
 
 Light 
 
 Hinged Ends... 
 
 11110 
 
 7500 
 
 5060 
 
 2C60 1800 
 
 1140 
 
 790 
 
 58C 
 
 420 
 
 r -60 
 
 Round Ends 
 
 10140 
 
 5950 
 
 3440 
 
 1760 
 
 1000 
 
 650 
 
 440 
 
 32C 
 
 230 
 
 41 1 
 
 Fixed Ends 
 
 12010 
 
 8730 
 
 6910 
 
 5310 
 
 3830 
 
 2660 
 
 1870 
 
 144C 
 
 1070 
 
 
 Flat Ends 
 
 12010 
 
 8730 
 
 6600 
 
 47301 3190 
 
 2260 
 
 1650 
 
 
 770 
 
 Heavy 
 
 Hinged Ends... 
 
 11380 
 
 7830 
 
 5390 
 
 2460 2C20 
 
 1270 
 
 890 
 
 64( 
 
 470 
 
 r*= -63 
 
 Round Ends 
 
 10440 
 
 6310 
 
 3760 
 
 2040 
 
 1150 
 
 720 
 
 510 
 
 36C 
 
 250 
 
 A" 
 
 Fixed Ends 
 
 11130 
 
 7770 
 
 5750 
 
 3890 
 
 2520 
 
 1690 
 
 1200 
 
 87( 
 
 
 * 
 
 Flat Ends 
 
 11130 
 
 7730 
 
 5280 
 
 32-0 
 
 2160 
 
 1430 
 
 880 
 
 53(, 
 
 
 Light 
 
 Hinged Ends... 
 
 10420 
 
 6590 
 
 4C60 
 
 2060 
 
 1200 
 
 770 
 
 540 
 
 35C 
 
 
 r -si 
 
 Round Ends 
 
 9290 
 
 4960 
 
 2470 
 
 1180 
 
 680 
 
 430 
 
 290 
 
 200 
 
 
 
 0" 
 
 Fixed Ends 
 
 11670 
 
 8370 
 
 6620 
 
 4910 
 
 3400 
 
 2310 
 
 1660 
 
 1240 
 
 940 
 
 O 
 
 Flat Ends 
 
 11670 &370 
 
 6210 
 
 4260 
 
 2830 
 
 2000 
 
 1390 
 
 920 
 
 600 
 
 Heavy. . . 
 
 r-= -59 
 
 Hinged Ends... 
 Round Ends 
 
 11010 
 10020 
 
 7430 
 
 5880 
 
 5010 
 3390 
 
 2970 
 1710 
 
 1730 
 960 
 
 1100 
 630 
 
 760 
 420 
 
 560 
 300 
 
 390 
 210 
 
 0" 
 
 Fixed Ends... 
 
 11310 
 
 7900 
 
 5960 
 
 4130 
 
 2730 
 
 1810 
 
 1320 
 
 960 
 
 710 
 
 O 
 
 Flat Ends 
 
 11310 7870 5520 
 
 3460 
 
 2320 
 
 1580 1000 
 
 630 
 
 400 
 
 Light 
 
 Hinged Ends... 
 
 10620 
 
 6780 4300 
 
 2220 
 
 1310 
 
 850 590 
 
 410 
 
 260 
 
 r -53 
 
 Round Ends. . . . 
 
 9530 
 
 5160 2690 
 
 1290 
 
 740 
 
 480 320 
 
 220 
 
 160 
 
TABLES OF STEUTS. 135 
 
 ROLLED ANGLES AS STRUTS. 
 
 Tables Nos. 9 and 10 apply to even-legged angles acting as 
 struts. As described in the head notes, the angle is considered 
 free to yield in its weakest direction, that is in the direction 
 of the least radius of gyration. 
 
 If the angle is prevented from failing in this direction, by 
 bracing or otherwise, its resistance will be increased to some ex- 
 tent, and a correction can be made by taking the greatest instead 
 of the least radius of gyration into the calculation. 
 
 Example. An angle strut with flat ends, whose dimensions 
 are 4 x 4 x | inches, and 13 feet long, has a least radius of gyra- 
 tion of . 81 inch, and greatest radius of gyration 1 . 24. When 
 
 7 144 
 
 the strut has no lateral support the value of would be = 
 
 178. (See table on page 98.) By Table No. 2 the safe load 
 would be 3,580 Ibs. per square inch. 
 
 If this strut it now braced so that it cannot fail in the weakest 
 direction, that is in the line of a diagonal from the corner of the 
 angle, but is free to fail in the direction of its legs, then the 
 
 I 144 
 
 value of becomes = 116, and the safe load by the tables 
 
 becomes 6,500 Ibs. per square inch. 
 
 STRUTS COMPOSED OF SEVERAL ANGLES. 
 If a strut is composed of several angles, properly braced to- 
 gether, so that the angles cannot fail individually, find the least 
 radius of gyration of the section in the manner described on 
 page 111, and thus the working resistance of the strut from 
 Table No. 2, as described before. 
 
 3 " Example. What is the working resistance 
 
 ^1 of a flat-ended strut 10" square outside, and 
 
 U 18 feet long, composed of four 3x3 angles 
 
 ^ 10" > connected by triangular bracing ? 
 
 k The radius of gyration as found on page 
 
 , 'I 111, is 4. 21 inches. 1=51. 
 
 T 
 
 Safe load per square inch by Table No. 2 = 10,800 Ibs. 
 
136 WKOUGHT IRON AND STEEL. 
 
 But the angles will fail individually if the bracing is not suf- 
 ficient. To determine the greatest distance apart for centres of 
 bracing, consider each angle as a strut bearing 10,800 Ibs. per 
 square inch of section. The least radius of gyration for a single 
 
 angle is . 60 inch. By Table No, 2, the value of correspond- 
 
 r 
 
 ing to the pressure of 10,800 is 51, as found above. Therefore 
 .60 x 51 = 30 inches, which is the greatest distance apart for 
 centres of bracing. For properly designed struts of the fore- 
 going section, the resistance per square inch may be ascertained 
 approximately by means of table No. 18, page 158, although the 
 former kind of column should be somewhat stronger than the 
 latter per unit of section. 
 
 STRUTS OF UNEVEN ANGLES. 
 
 When uneven angles are used as struts, find the value of 
 
 r 
 
 by means of the least radius of gyration as found on page 99, 
 and the corresponding resistance per square inch of section by 
 table No. 2 as before. If the angle is braced in such a manner 
 that failure cannot occur diagonally, it will then fail in the di- 
 rection of the shortest leg, and if braced in this direction also, 
 it will be forced to fail in the direction of the longest leg. The 
 resistance in either direction can readily be found by means of 
 the respective radii of gyration, as given in columns VII, VIII, 
 IX, page 99. 
 
 It is frequently desirable to use a pair of uneven angles, 
 braced together in the direction of the shortest legs. 
 
 Total length = L. 
 
 v\S \P 
 
 f- -----I' 
 
 For this form the least radius of gyration for the combined 
 
TABLES OF STEUTS. 137 
 
 sections will be the same as the greatest radius of gyration for a 
 single angle. Therefore take in the tables of elements of un- 
 even angles, the greatest radius, or that corresponding to axis 
 A B, when estimating the strength of the combined sections, 
 and the least radius when determining the distance between cen- 
 tres of bracing. 
 
 Example. A flat-ended strut, 16 feet long, is composed of 
 two uneven angles, each 6 x 4 x ^ inches, and 4.75 square 
 inches sectional area. The angles are braced together in the 
 direction of the short legs. What is the greatest safe load for 
 the strut, and what the greatest distance between centres of 
 bracing measured on the leg of the angle ? 
 
 By the tables on page 99, the greatest radius of gyration = 
 
 1.9 inches, therefore L = 101. 
 
 T 
 
 By Table No. 2 we have for this 7,450 Ibs. per square inch, 
 or 70,700 Ibs. for the whole strut. The least radius of gyration 
 is .92 inch, which multiplied by 101 gives 92.9 inches as the 
 greatest distance between centres of bracing. 
 
 To find the greatest distance apart centres of bracing (I) should 
 
 be it is only necessary to remember that should not exceed - . 
 
 I = distance between bracing centres. 
 
 r = least radius of gyration of single angle. 
 
 L total length of strut. 
 
 E = least radius of gyration of combined section. 
 
 When struts of any section are hinged, in order to utilize the 
 maximum efficiency of the strut it is of the utmost importance 
 to keep the centre of pin in line with the centre of gravity of 
 cross section of the strut. In the tables of elements 94-101, the 
 positions of centres of gravity are accurately defined. 
 
138 
 
 TABLES OF STRUTS. 
 
 No. 9, 
 PENCOYD ANGLES AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION USING 
 THE FACTORS OF SAFETY OF PREVIOUS TABLES. 
 
 SIZE OP ANGLE. 
 
 CONDITION OP 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 4870 
 422.1 
 2930 
 1690 
 
 18 
 
 6"x 6" 
 
 r= 1-18 
 
 Fixed Ends... 
 Flat Ends 
 Hinged Ends. .. 
 Round Ends 
 
 14380 
 14:380 
 13940 
 13330 
 
 11670 
 11670 
 11010 
 10020 
 
 9920 
 9920 
 9140 
 7720 
 
 8370 
 8370 
 7430 
 5880 
 
 7410 
 7330 
 6100 
 4440 
 
 6580 
 6160 
 4960 
 3340 
 
 5710 
 5230 
 4010 
 2430 
 
 4060 
 3400 
 2180 
 1260 
 
 5"x5" 
 
 r = -99 
 
 Fixed Ends .. 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 13840 
 1:3840 
 13330 
 12670 
 
 11040 
 11040 
 10330 
 9170 
 
 8960 
 8960 
 8080 
 6580 
 
 7630 
 7590 
 6410 
 4760 
 
 6620 
 6210 
 5010 
 3390 
 
 5590 
 5080 
 3840 
 2310 
 
 4570 
 3920 
 2640 
 1530 
 
 3690 
 3070 
 1930 
 1090 
 
 2940 
 2480 
 1430 
 810 
 
 4"x 4" 
 
 r = -80 
 
 Fixed Ends 
 Flat Ends 
 Hinged En ds... 
 Round Ends. . . . 
 
 13030 
 13030 
 12460 
 11670 
 
 10090 
 10090 
 9320 
 7930 
 
 8000 
 7970 
 6910 
 5200 
 
 6750 
 6370 
 5170 
 3540 
 
 5470 
 4930 
 3680 
 2190 
 
 4250 
 3580 
 2320 
 1350 
 
 3280 
 2730 
 1650 
 920 
 
 2470 
 2120 
 1170 
 670 
 
 1870 
 1650 
 890 
 510 
 
 3f'x 3f 
 
 r = -69 
 
 Fixed Ends 
 Flat Ends 
 
 12520 
 12520 
 11920 
 11060 
 
 9270 
 9270 
 8420 
 6950 
 
 7370 
 7270 
 6040 
 4380 
 
 5920 
 5470 
 4250 
 2640 
 
 45?,0 
 '3870 
 2600 
 1500 
 
 asio 
 
 2760 
 1(570 
 930 
 
 2410 
 2070 
 1140 
 650 
 
 1790 
 1550 
 830 
 470 
 
 1400 
 1090 
 620 
 350 
 
 Hinged Ends. .. 
 Round Ends 
 
 3"x3" 
 
 r = 59 
 
 Fixed Ends.... 
 Flat Ends 
 Hinged Ends... 
 Round Ends. . . . 
 
 11760 
 11760 
 11110 
 10140 
 
 8420 
 8420 
 7500 
 5950 
 
 6670 
 6260 
 5060 
 3440 
 
 5000 
 4350 
 3060 
 1760 
 
 3500 
 
 2900 
 
 2410 
 
 2070 
 1140 
 650 
 
 1720 
 1460 
 790 
 440 
 
 1290 
 970 
 580 
 320 
 
 980 
 650 
 420 
 230 
 
 2J"x2f" 
 
 r = -64 
 
 Fixed Ends... 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 11400 
 11400 
 10720 
 9660 
 
 8090 
 8070 
 7040 
 5350 
 
 6170 
 5740 
 4530 
 2910 
 
 4370 
 3710 
 2440 
 1420 
 
 2480 
 1430 
 810 
 
 1940 
 1730 
 9:30 
 540 
 
 1440 
 1140 
 640 
 360 
 
 1040 
 720 
 450 
 240 
 
 780 
 460 
 300 
 170 
 
 2f x2f 
 
 T = -49 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 11040 
 11040 
 10830 
 
 9170 
 
 7680 
 7640 
 6470 
 4830 
 
 5630 
 5130 
 3900 
 2350 
 
 3760 
 3K30 
 1970 
 1120 
 
 2410 
 2070 
 1140 
 650 
 
 1630 
 1350 
 740 
 410 
 
 1130 
 830 
 510 
 270 
 
 830 
 490 
 320 
 190 
 
 II" 
 
TABLES OF STRUTS. 
 
 139 
 
 No. 9. 
 PENCOYD ANGLES AS STRUTS. 
 
 A 
 
 B 
 
 </ ^ 
 
 The radius of gyration is taken about the axis A B, which also indicates the 
 direction of pin if the strut is hinged. 
 r in marginal columns indicates radius of gyration around axis A B. 
 
 LENGTH IN FEET. 
 
 CONDITION OP 
 ENDS. 
 
 SIZE OF ANGLE. 
 
 20 
 
 3400 
 
 283!) 
 1730 
 960 
 
 2360 
 2030 
 1120 
 640 
 
 1540 
 1250 
 690 
 380 
 
 1070 
 770 
 470 
 250 
 
 740 
 430 
 280 
 170 
 
 22 
 
 2780 
 2360 
 1340 
 760 
 
 1870 
 1(550 
 890 
 510 
 
 1230 
 910 
 550 
 300 
 
 870 
 530 
 350 
 200 
 
 24 
 
 26 
 
 28 
 
 1660 
 1390 
 760 
 420 
 
 1100 
 800 
 490 
 260 
 
 680 
 380 
 240 
 150 
 
 30 
 
 1440 
 1140 
 640 
 360 
 
 950 
 620 
 400 
 220 
 
 32 
 
 1240 
 920 
 560 
 300 
 
 810 
 470 
 310 
 
 180 
 
 34 
 
 1060 
 750 
 460 
 240 
 
 690 
 390 
 250 
 
 150 
 
 36 
 
 940 
 600 
 390 
 210 
 
 2310 
 2000 
 1100 
 630 
 
 1590 
 1310 
 720 
 400 
 
 1000 
 670 
 430 
 230 
 
 690 
 390 
 250 
 150 
 
 1910 
 1690 
 910 
 530 
 
 1340 
 
 1020 
 600 
 330 
 
 820 
 490 
 320 
 190 
 
 Fixed Ends... 
 Flat Ends 
 Hinged Ends... 
 Round Ends.... 
 
 Fixed Ends 
 Flat Ends .... 
 
 6"x 6" 
 
 5"*5" 
 4"x4" 
 3f x3" 
 3"x3" 
 
 2f"x2f" 
 2-1." X2-J-" 
 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 
 
 
 
 
 
 
 
 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends.... 
 
 Fixed Ends 
 Flat, Ends 
 Hinged Ends... 
 Round Ends.... 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends.... 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
140 
 
 TABLES OF STEUTS. 
 
 No. 10. 
 PENCOYD ANGLES AS STRUTS. 
 
 GREATEST SAFE LOADS IN LBS. PER SQUARE INCH OF SECTION. 
 (See remarks at head of Table No. 9.) 
 
 
 CONDITION or 
 
 LENGTH IN FEET. 
 
 
 ENDS. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 2J"x 2 f 
 
 Fixed Ends.... 
 Flat Ends 
 
 10600 
 10600 
 
 7190 
 7020 
 
 5000 
 4350 
 
 3090 
 
 2600 
 
 187C 
 165(1 
 
 129C 
 970 
 
 89C 
 
 55T 
 
 640 
 
 ' 340 
 
 .... 
 
 . . 
 
 
 Hinged Ends.. 
 
 9860' 5800 
 
 3060 
 
 1530 
 
 890 
 
 580 360 230 .... 
 
 r = -44 
 
 Round Ends. . . 
 
 8600 
 
 4150 
 
 1760 
 
 860 
 
 510 
 
 320 
 
 200 
 
 i 140 
 
 
 2"x 2" 
 
 Fixed Ends... 
 Flat Ends 
 
 10000 
 10000 
 
 6670 
 6260 
 
 4170 
 3500 
 
 2410 
 
 9070 
 
 1500 
 1200 
 
 980 
 fifin 
 
 660 
 
 irn 
 
 ... 
 
 .... 
 
 
 Hinged Ends... 
 
 9230 
 
 5060 
 
 2250 
 
 1140 
 
 670! 420' 230 
 
 
 
 r = -39 
 
 Round Ends 
 
 7820 
 
 3440 
 
 1310 
 
 650 
 
 370 
 
 230 
 
 150 
 
 
 ... 
 
 If'xlf 
 
 Fixed Ends 
 Flat Ends 
 
 9430 
 9430 
 
 6090 
 5650 
 
 3500 
 2900 
 
 1870 
 1650 
 
 1160 
 
 850 
 
 740 
 430 
 
 
 
 
 
 
 
 
 Hinged Ends... 
 
 8600 
 
 4440 
 
 1800 
 
 890 
 
 520 
 
 28o!:;;: 
 
 
 
 r = -35 
 
 found Ends 
 
 7140 
 
 2820 
 
 1000 
 
 510 
 
 380 
 
 17( 
 
 
 
 
 1 1 " V 11" 
 
 2 *" 
 
 Fixed Ends 
 Flat End* 
 
 8650 
 8650 
 
 5190 
 4590 
 
 2590 
 2210 
 
 1390 
 
 1080 
 
 810 
 
 480 
 
 
 
 
 
 
 
 
 
 
 linged Ends.. . 
 
 775C 
 
 3310 
 
 1230 
 
 620 
 
 310 
 
 
 
 
 
 T = '31 
 
 iound Ends 
 
 6220 
 
 194C 
 
 700 
 
 350 
 
 W 
 
 
 
 
 
 u." x ii" 
 
 <Mxed Ends 
 Flat Ends 
 
 7860 
 7830 
 
 4000 
 3340 
 
 1750 
 1500 
 
 920 
 
 580 
 
 
 
 
 
 
 
 
 
 
 
 *t ^ 
 
 Hinged Ends 
 
 6720 
 
 2130 
 
 810 
 
 *W) 
 
 
 
 
 
 
 T== -26 
 
 Round Ends 
 
 5100 
 
 1230 
 
 450 
 
 210 
 
 
 
 
 
 
 
 Fixed Ends 
 
 6670 
 
 2410 
 
 980 
 
 
 
 
 
 
 
 
 Flat Ends 
 
 6260 
 
 2070 
 
 650 
 
 
 
 
 
 
 
 
 
 5060 
 
 1140 
 
 420 
 
 
 
 
 
 
 
 r= -20 
 
 found Ends.... 
 
 3440 
 
 650 
 
 230 
 
 
 
 
 
 
 
 
 
 
 
 
 
TABLES OF STRUTS. 141 
 
 TEE STRUTS. 
 
 The following tables are for even tees. For single uneven tees, 
 find the least radius of gyration from the table of elements, page 
 101, and proceed as described for angle struts, on page 135. 
 
 When a pair of uneven tees are braced together in the direc- 
 tion of the shortest leg, they form a single strut, whose least 
 radius of gyration is the same as the greatest radius of gyration 
 for a single tee. 
 
 Therefore, when determining the resistance of the combined 
 strut, take the greatest radius of gyration from the table on page 
 101, and the least radius of gyration, when determining the dis- 
 tance between centres of lateral bracing. 
 
 Example. A. pair of uneven tees 5 x 2 inches, whose total 
 area is 6 . 1 square inches, are braced together in the direction of 
 the shortest leg, forming a single hinged-ended strut 15 feet 
 long. What is the greatest safe load, and what the greatest 
 distance between centres of lateral bracing ? 
 
 By table on page 101, greatest radius of gyration = 1.14 inches, 
 
 - = 158, which by Table No. 2 gives 3,100 Ibs. per square inch, 
 
 or 18,900 Ibs. total greatest safe load. 
 
 Least radius of gyration = .72, which multiplied by 158 gives 
 113 inches as the greatest distance between centres of lateral 
 bracing. 
 
TABLES OF STBUTS. 
 No. 11. 
 
 PENCOYD TEES AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 When the strut is free to fail in the direction C. D. Using factors of safety 
 given in previous table. 
 
 SIZE OP TEE. 
 
 CONDITION 
 
 OF 
 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 ,, ,, 
 
 Fixed Ends 
 
 13160 
 
 10260 
 
 8140 
 
 6910 
 
 5670 
 
 4530 
 
 
 rt * TC 
 
 Fiat Ends 
 
 13160 
 
 10260 
 
 8120 
 
 6600 
 
 5'80 
 
 3870! 2900 
 
 
 Hinged Ends... 
 
 12610 
 
 9500 
 
 7100] 5390 
 
 39.50 
 
 2600 
 
 1800 
 
 r = -84 
 
 Round Ends 
 
 11840 
 
 8150 
 
 5420 3760J 2390 
 
 1500 
 
 1000 
 
 Q 1 " v Q 1 " 
 
 Fixed Ends 
 
 12780 
 
 9590 
 
 7630 
 
 6220 4910 
 
 3660 
 
 2710 
 
 O^" A Ocj- 
 
 Flat Ends.. ... 
 
 12780 
 
 9590 
 
 7590 
 
 5790 
 
 4260 
 
 8040 
 
 2300 
 
 
 Hinged Ends... 
 
 12190 
 
 8780 
 
 6410 
 
 4580 
 
 2970 
 
 1910 
 
 1300 
 
 r = -74 
 
 Round Ends 
 
 11360 
 
 7330 
 
 4760 
 
 2960 
 
 1710 
 
 1070 
 
 740 
 
 8" x f \" 
 
 Fixed Ends.... 
 
 11890 
 
 8650 
 
 6830 
 
 5190 
 
 3690 
 
 2590 
 
 1820 
 
 o xs o 
 
 Flat Ends 
 
 11890 
 
 8650 
 
 6490 
 
 4590 
 
 3070 
 
 2210 
 
 1590 
 
 
 Hinged Knds... 
 
 11240 
 
 7750 
 
 5280 
 
 3310 
 
 193o! 1230 
 
 860 
 
 r =* -62 
 
 Round Ends 
 
 10290 
 
 6220 
 
 3650 
 
 1940 
 
 1090 
 
 700 
 
 490 
 
 O 1 " y O 1 " 
 
 Fixed Ends... 
 
 11400 
 
 8090 
 
 6170 
 
 4370 
 
 2940 
 
 1930 
 
 1440 
 
 ^^ ^ ^^ 
 
 Flat Ends 
 
 11400 
 
 8070 
 
 5740 
 
 3710 
 
 2480 
 
 1720 
 
 1140 
 
 
 Hinged Ends... 
 
 10720 
 
 7040 
 
 4530 
 
 2440 
 
 1430 
 
 920 
 
 640 
 
 r = -65 
 
 Round Ends 
 
 9660 
 
 5350 
 
 2910 
 
 1420 
 
 810 
 
 540 
 
 360 
 
 O 1 " X O 1 " 
 
 Fixed Ends 
 
 10770 
 
 7410 
 
 5270 
 
 3370 
 
 2070 
 
 14:30 
 
 990 
 
 ^47 ^ ^47 
 
 Flat Ends 
 
 10770 
 
 7330 
 
 4680 
 
 2800 
 
 1830 
 
 1120 
 
 670 
 
 
 Hinged Ends. .. 
 
 10040 
 
 6100 
 
 3410 
 
 1710 
 
 990 
 
 640 
 
 420 
 
 r = -47 
 
 Round Ends 
 
 8820 
 
 4440 
 
 2010 
 
 950 
 
 570 
 
 350 
 
 230 
 
 2" x 2" 
 
 Fixed Ends 
 
 10340 
 
 6990 
 
 4690 
 
 2800 
 
 1730 
 
 1140 
 
 790 
 
 
 Flat Ends 
 
 10340 
 
 6720 
 
 4040 
 
 2380 
 
 1470 
 
 840 
 
 460 
 
 
 Hinged Ends. .. 
 
 9590 
 
 5500 
 
 2760 
 
 1350 
 
 790 
 
 510 
 
 300 
 
 r = -43 
 
 Round Ends 
 
 8260 
 
 3870 
 
 1590 
 
 760 
 
 440 
 
 270 
 
 170 
 
 1 3" v 13" 
 
 Fixed Ends... 
 
 9590 
 
 6220 
 
 3660 
 
 1980 
 
 1250 
 
 800 
 
 
 f 47 
 
 Flat Ends 
 
 9590 
 
 5790 
 
 3040 
 
 1760 
 
 930 
 
 470 
 
 
 
 Hinged Ends. .. 
 
 8780 
 
 4580 
 
 1910 
 
 950 
 
 560 
 
 810 
 
 
 r = -87 
 
 Round Ends 
 
 7330 
 
 2960 
 
 1070 
 
 550 
 
 300 
 
 180 
 
 
 "11" 11" 
 
 Fixed Ends. 
 
 8800 
 
 5390 
 
 2760 
 
 1500 
 
 'm 
 
 
 -"'F * ^ 
 
 Flat Ends.. '. ... 
 
 8800 
 
 4830 
 
 2340 
 
 1200 
 
 540 
 
 
 
 
 Hinged Ends. .. 
 
 7910 
 
 3570 
 
 1330 
 
 670 
 
 360 
 
 
 
 r =. .33 
 
 Round Ends 
 
 6400 
 
 2120 
 
 750 
 
 370 
 
 200 
 
 
 
 
 
TABLES OF STKUTS. 
 
 No. 11. 
 PENCOYD TEES AS STRUTS. 
 
 ;A 
 
 143 
 
 'D 
 
 Radius of gyration taken around axis A. B. which also indicates the direc- 
 tion of pin when strut is hinged, r in marginal columns indicates radius of 
 gyration around axis A. B. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 OF 
 
 ENDS. 
 
 SIZE OF TEE. 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 2660 
 &*60 
 
 1270 
 730 
 
 1980 
 1760 
 950 
 550 
 
 1400 
 1090 
 620 
 350 
 
 1040 
 720 
 450 
 240 
 
 700 
 400 
 260 
 160 
 
 2020 
 1790 
 970 
 560 
 
 1580 
 1300 
 710 
 400 
 
 1050 
 730 
 450 
 240 
 
 780 
 4.50 
 300 
 170 
 
 1650 
 1380 
 750 
 420 
 
 1250 
 9130 
 560 
 300 
 
 810 
 480 
 310 
 180 
 
 1350 
 1030 
 600 
 330 
 
 990 
 670 
 420 
 230 
 
 107C 
 
 770 
 470 
 250 
 
 800 
 470 
 310 
 180 
 
 910 
 
 570 
 370 
 200 
 
 740 
 
 430 
 280 
 170 
 
 Fixed Ends... 
 FJat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 
 4"x4" 
 
 r == -84 
 
 3J" x 31" 
 
 r = -74 
 
 3"x 3" 
 
 r == -02 
 
 21" x 21" 
 
 r = -65 
 
 2i"x2J" 
 
 r = -47 
 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends .. 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends.... 
 Flat Ends 
 Hineed Ends... 
 Round Ends 
 
 Fixed Ends.... 
 Flat Ends 
 Hinged Ends... 
 Round Ends.... 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 SIZE OF TEE. 
 
 CONDITION 
 OF ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 H"x if 
 
 r = -27 
 
 l"x 1" 
 
 r = '2 
 
 Fixed Ends.... 
 Flat Ends 
 Hinsred Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 8000 
 7970 
 6910 
 5200 
 
 7860 
 7830 
 6720 
 5100 
 
 4250 
 3'80 
 2320 
 1350 
 
 4000 
 3340 
 2130 
 1230 
 
 1870 
 1650 
 890 
 . 510 
 
 1750 
 1500 
 810 
 450 
 
 1000 
 670 
 430 
 230 
 
 920 
 580 
 380 
 210 
 
 
 
 
 
 
 
 
 
 
 
 
 
 :::::: 
 
 
 
 
 
 
 
 
 
144 
 
 TABLES OF STRUTS. 
 
 No. 12. 
 LATTICED CHANNEL STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION, 
 USING FACTORS OF SAFETY GIVEN IN PREVIOUS TABLES. Q 
 
 For a pair of braced channel? or for a single channel secured from 
 flexure in the direction of the flanges and liable 10 fail only in the 
 direction of the web C />. A- 
 
 r in the marginal columns gives the radius of gyration for axis 
 A B, or for either axis of the combined pair of channels. See de- 
 scription, page 121. 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OP 
 
 OF 
 
 
 
 
 
 
 
 
 
 CHANNEL 
 
 ENDS. 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 15" 
 
 Fixed Ends 
 
 
 
 14110 
 
 13570 
 
 12900 
 
 12400 
 
 11890 
 
 11400 
 
 11040 
 
 
 Flat Ends 
 
 
 14110 
 
 1357d 
 
 12900 12400 11890 11400 
 
 iimn 
 
 ia7 
 
 Hinged Ends... 
 
 
 ..13640 
 
 13050 
 
 12320 11780 11240 10720 10330 
 
 
 
 Round Ends. 
 
 
 luunn 
 
 1233,) 
 
 11520 10900 10290 9(i(iO 
 
 9HO 
 
 
 
 
 
 2.05 
 
 2.46 
 
 2.87 
 
 3.28 3.69 
 
 4.10 
 
 4.51 
 
 12"H'y 
 
 Fixed Ends 
 
 
 14240 
 
 13570 
 
 12780 
 
 12140 ! 11580 
 
 11130 
 
 10600 
 
 10170 
 
 
 Flat Ends 
 
 
 14240 13570 
 
 12780 
 
 12140 11580 11130 
 
 10600 
 
 10170 
 
 10-3 
 
 J V 
 
 Hinged Ends. .. 
 
 
 13790 13050 12190 
 
 115101091010420 
 
 9860 9410 
 
 d 7-5 
 
 Round Ends 
 
 
 13160 
 
 12330 
 
 11360 
 
 10600J 9900: 9290 
 
 8600 8J40 
 
 
 
 
 1.61 
 
 2.02 
 
 2.42 
 
 2.83! 3.23 
 
 3.64 
 
 4.C4 
 
 4.44 
 
 12"L't 
 
 Fixed Ends.... 
 
 
 14240 
 
 13570 
 
 12780 
 
 1214011580 
 
 11130 
 
 10600 
 
 10170 
 
 r ==== 4 66 
 
 Flat Ends 
 
 
 14240 
 
 13570 
 
 12780 
 
 12140115801113010600 
 
 10170 
 
 J) - = 10-2 
 
 Hinged Ends... 
 
 
 1379;) 
 
 13350 
 
 1219:) 
 
 11510;i0910;i0420 
 
 9860 
 
 9410 
 
 d = 7-7 
 
 Round Ends 
 
 
 
 13160 
 
 1233:) 
 
 11360 
 
 10600 9900 9290 
 
 8600 
 
 8040 
 
 
 
 
 1.30 
 
 1.62 
 
 1.94 
 
 2.27 2.59 2.92 
 
 3.24 
 
 3.16 
 
 10"lTy 
 
 Fixed Ends 
 
 
 1:3840 
 
 isnn 
 
 12140 
 
 11490 10950 
 
 10430 
 
 9920 
 
 9430 
 
 
 Flat Ends . 
 
 
 13840 12900 12140 
 
 11490 10950 10430 
 
 9920 
 
 ()4;->Q 
 
 r = 3 "92 
 
 Hinged Ends 
 
 
 13350 12320 11510 
 
 10820 10230 9680 
 
 9140 
 
 8COO 
 
 D= 9 * 
 
 Round Ends. 
 
 , 
 
 12670 1 ifwn lOfino 
 
 9780, 9050 8370 
 
 77 -'0 
 
 7140 
 
 d i==s 6 3 
 
 
 
 1.71 
 
 2.14 
 
 2.57 
 
 2.99 3.42 3.85 
 
 4.28 
 
 4.71 
 
 10"L't 
 
 Fixed Ends 
 
 
 13700 
 
 12900 
 
 12140 
 
 11490 
 
 10950 
 
 10340 
 
 9840 
 
 9350 
 
 
 Flat Ends 
 
 
 13700 12900 
 
 12140 114UH 
 
 10950 
 
 10340 
 
 9840 
 
 9350 
 
 r ~^= 3 8 9 
 
 D= B ' 
 
 Hinged Ends... 
 Round Ends 
 
 
 13200 12320 
 12500J 11520 
 
 11510 
 10600 
 
 10820 
 9780 
 
 10230 
 9050 
 
 9590 
 8260 
 
 9050 
 7630 
 
 8510 
 7040 
 
 
 
 
 1.42 
 
 1.77 
 
 2.13 
 
 2.48 
 
 2.84 
 
 3.19 
 
 3.55 
 
 3.90 
 
 9"He'vy 
 
 Fixed Ends 
 
 14240 
 
 13300 
 
 12400 
 
 11580 
 
 10950 
 
 10340 
 
 9760 
 
 9190 
 
 8650 
 
 r = 3-45 
 
 Flat Ends 14240 13300 12400 
 
 11580 
 
 10950 
 
 10340 
 
 9760 
 
 9190 
 
 8(>50 
 
 D- 8>1 
 d = 6-4 
 
 Hinged Ends. ..13190,12760 11780 
 Round Ends. ... 131(50 12000 l'900 
 
 10910 
 9900 
 
 10230 
 9050 
 
 9590 
 8260 
 
 8960 
 7530 
 
 83 
 6850 
 
 7750 
 6220 
 
 
 1.18 1.53 
 
 1.97 
 
 2.36 
 
 2.76 
 
 3.15 
 
 3.55 
 
 3.94 
 
 4.33 
 
 9 "Light 
 
 Fixed Ends.... 
 
 14240 
 
 13300 
 
 12400 
 
 11580 
 
 10950 
 
 10340 
 
 9760 
 
 9190 
 
 8650 
 
 7-8 
 
 Flat Ends .14340,13300 12400 11580 10950 
 Hinged Ends.. .13790 12760 1178()il0910!10230 
 
 10340 
 9590 
 
 9760 
 89(50 
 
 01 '.'0 
 8330 
 
 8H5i 1 
 7750 
 
 
 d = 5- 8 
 
 Round Ends. . . . 131HO; 12000 10900 
 
 99001 9050 
 
 8260 
 
 7530 
 
 6850 
 
 6220 
 
 
 
 1.03 
 
 1.38 
 
 1.72 
 
 2.06 2.41 
 
 2.75 
 
 3.10 
 
 M, 
 
 3.78 
 
TABLES OF STRUTS. 
 
 145 
 
 No. 12. 
 LATTICED CHANNEL STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION, 
 USING FACTORS OF SAFETY GIVEN IN PREVIOUS TABLES. 
 
 The channels must be connected so as to 
 insure unity of action and separated not 
 less than the distances D or d respectively, 
 given in inches in the marginal columns. 
 Figures in heavy type under each length 
 represent the greatest distances apart in 
 feet on each channel that centres of lateral 
 bracing should be placed. 
 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 SIZE 
 
 
 
 
 
 
 
 
 
 
 OF 
 
 OF 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 ENDS. 
 
 CHANNEL. 
 
 10690 
 
 10260 
 
 9920 
 
 9590 
 
 9190 
 
 8880 
 
 8580 
 
 8280 
 
 8090 
 
 Fixed Ends 
 
 15" 
 
 10690 
 
 10260 9920 9590 
 
 9190 
 
 8880! 8580 
 
 8270 
 
 807'0 
 
 Flat Ends 
 
 r = 5. 51 
 
 9950 
 
 9500| 9140 8780 
 
 8330 8000j 7670 
 
 7300 
 
 7040 
 
 Hinged Ends... 
 
 
 8710 
 
 8150 7720 7330 
 
 6850 6490 1 6130 
 
 5730 
 
 5350 
 
 Round Ends . . . 
 
 D 
 
 4.92 
 
 5.33 
 
 5.74 6.15 
 
 6.56 
 
 6.97 
 
 7.38 
 
 7.79 
 
 8.20 
 
 
 
 9760 
 
 9270 
 
 8880 8500 
 
 8230 
 
 7950 
 
 7720 
 
 7500 
 
 7240 
 
 Fixed Ends.... 
 
 12"H'y 
 
 9760 
 
 9270 
 
 8880 8500 
 
 822(, 
 
 7920 
 
 7680 
 
 7450 
 
 7080 
 
 Flat Ends ... 
 
 r = 4 -56 
 
 8960 
 
 8420 
 
 8000 7580 
 
 7240 
 
 6840 
 
 6530 
 
 6220 
 
 5860 
 
 Hinged Ends.. 
 
 
 7530 
 
 6950 
 
 6490 6040 
 
 5CGO 
 
 5230 
 
 4890 
 
 4560 
 
 4210 
 
 Round Ends 
 
 d= 7 . 5 
 
 4.85 
 
 5.25 
 
 5.66 6.06 
 
 6.47 6.87 
 
 7.28 
 
 7.68 
 
 8.09 
 
 
 
 9760 
 
 9270 
 
 8880 8500 
 
 8230 
 
 7950 
 
 7720 
 
 7500 
 
 7280 
 
 Fixed Ends... 
 
 12' Vt 
 
 9760 
 
 9270 
 
 8880 8500 
 
 8220 
 
 7920 
 
 7680 
 
 7450 
 
 7140 
 
 Flat Ends 
 
 r - 4.56 
 
 8960 
 
 8420 
 
 8000 7580 
 
 7240 
 
 6840 
 
 6530 
 
 6220 
 
 5920 
 
 Hinged Ends... 
 
 -r\ 10-2 
 
 7530 
 
 6950 
 
 6490 6040 
 
 5660 
 
 5230 
 
 4890 
 
 4560 
 
 4270 
 
 Round Ends 
 
 
 3.89 
 
 4.21 
 
 4.54 
 
 4.86 
 
 5.19 
 
 5.51 
 
 5.84 
 
 6.16 
 
 6.49 
 
 
 8960 
 
 8420 
 
 8140 
 
 7860 
 
 7590 
 
 7320 
 
 7070 
 
 6830 
 
 6580 Fixed Ends... 
 
 10"H'y 
 
 8960 
 
 8420 8120 
 
 7830 
 
 7540 
 
 7210i 6840 6490 
 
 6160 Flat Ends... 
 
 
 8080 
 
 7500 7100 
 
 6720 
 
 6340 
 
 5>80 5620 5280 
 
 4960 Hinged Ends... 
 
 D'I -<t 
 
 6580 
 
 5950 
 
 5420 
 
 5100 
 
 4690 
 
 4320 3980 3650 
 
 3340 Round Ends. . . 
 
 = V V 
 
 j=r= 6-3 
 
 6.13 
 
 5.56 
 
 5.99 
 
 6.42 
 
 6.85 
 
 7.28 
 
 7.71 
 
 8.14 
 
 8.57 
 
 
 
 880 
 
 8420 
 
 8140 
 
 7810 
 
 7540 
 
 7280 
 
 7030 
 
 6790 
 
 6530 
 
 Fixed Ends... 
 
 10"L't 
 
 8880 
 
 8420 
 
 8120 
 
 7780 7500 
 
 7140 6780J 6430 
 
 6110 Flat Ends 
 
 r =^ 3* 89 
 
 8000 
 
 7500 
 
 7100 
 
 6650 
 
 6280 
 
 5920 5560 5220 
 
 41)10 Hineed Ends... 
 
 
 6490 
 
 5950 
 
 5420 
 
 5030 
 
 4630 
 
 4270 3920; S600 
 
 3290 
 
 Round Ends 
 
 d_-_ 0-3 
 
 4.26 
 
 4.61 
 
 4.97 
 
 5.32 
 
 5.68 
 
 6.03 
 
 6.391 6.74 
 
 7.10 
 
 
 
 8280 
 
 7950 
 
 7630 
 
 7320 
 
 7030 
 
 6750 
 
 6440 
 
 6130 
 
 5840 
 
 Fixed Ends... 
 
 9"He'vy 
 
 8270 
 
 7920 
 
 7590 
 
 7210 
 
 6780 
 
 6370 6020 
 
 5700 
 
 5380 
 
 Flat Ends 
 
 r =- 3 45 
 
 7300 
 
 6840 6410 
 
 5980 
 
 5560 
 
 5170| 4820 
 
 4480 
 
 4160 
 
 Hinged Ends... 
 
 
 5730 5230 4760 
 
 4320 3920 
 
 3540 ! 3200 
 
 2870 
 
 2550 
 
 Round Ends 
 
 D= w-1 
 
 <jr= 6 - 4 
 
 4.73 
 
 5.12 
 
 5.52 
 
 5.91 
 
 6.30 
 
 6.70 
 
 7.09 
 
 7.49 
 
 7.88 
 
 
 
 8230 
 
 7900 
 
 7590 
 
 7280 
 
 6990 
 
 6710 
 
 6400 
 
 6090 
 
 6800 
 
 Fixed Ends 
 
 9 "Light. 
 
 8220 7870 
 
 7540 
 
 7140 6720 6310 5970 5650 
 
 5340 
 
 Flat, Ends r = 3 7 43 
 
 7240 678d 
 
 6340 5920 5500 5110 4770 ! 4440 
 
 4120 
 
 Hinged Ends...! ^ ,. u 
 
 5660 
 
 5160 
 
 4690 4270 
 
 3870 3490 8150 2820 
 
 2510 
 
 Round Ends 
 
 d= 6*8 
 
 4.13 
 
 4.47 
 
 4.82 
 
 5.16 
 
 5.50 
 
 5.85 
 
 6.19 
 
 6.54 
 
 6.88 
 
 
 
 11 
 
146 
 
 TABLE OF STRUTS. 
 
 NO. 13. 
 LATTICED CHANNEL STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION, 
 USING FACTORS OF SAFETY GIVEN IN PREVIOUS TABLES. 
 
 For a pair of braced channels or for a single channel secured from 
 flexure in the direction of the flanges and liable to fail only in the 
 direction of the web C I). 
 
 r in the marginal columns gives the radius of gyration for axis 
 A JB, or for either axis of the combined pair of channels. See de- 
 scription, page 121. 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OF 
 
 OP 
 
 
 
 
 
 
 
 
 
 CHANNEL 
 
 ENDS. 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 8"He'vy 
 
 Fixed Ends 
 
 
 13840 
 
 12900 
 
 11890 
 
 11130 
 
 10430 
 
 9760 
 
 9190 
 
 8580 
 
 
 Flat Ends 
 
 
 13840 
 
 129001189011130 
 
 10430 
 
 9760 9190 
 
 8580 
 
 7-2 
 
 Hinged Ends... 
 
 
 
 13350 
 
 123201124010420 
 
 9680 
 
 8900 8330 
 
 7670 
 
 
 d = 4*8 
 
 Round Ends . . . 
 
 
 12670 
 
 11520 10290 
 
 9290 
 
 8370 
 
 7530; 6850 
 
 6130 
 
 
 
 
 1.39 
 
 1.86 
 
 2.32 
 
 2.78 
 
 3.25 
 
 3.71 
 
 4.18 
 
 4.64 
 
 8 "Light 
 
 Fixed Ends 
 
 
 13970 
 
 12900 
 
 11890 
 
 11130 
 
 10520 
 
 9810 
 
 9190 
 
 8580 
 
 
 Flat Ends 
 
 
 13970 
 
 12900 11890 11130 
 
 10520 
 
 9840' 9190 
 
 8580 
 
 r 3*09 
 
 Hinged Ends 
 
 
 13500 
 
 12320 11240 
 
 10420 
 
 9770 
 
 9050 8330 
 
 7670 
 
 D = 7-1 
 
 d 5-0 
 
 Round Ends 
 
 
 12830 
 
 11520 10290 
 
 9290 
 
 8490 
 
 7630 6850 
 
 6130 
 
 
 
 
 1.16 
 
 1.55 
 
 1.94 
 
 2.33 
 
 2.72 
 
 3.10 3.49 
 
 3.88 
 
 7"He'vy 
 
 Fixed Ends.... 
 
 
 13430 
 
 12270 
 
 11310 
 
 10520 
 
 9760 
 
 9040 8370 
 
 7950 
 
 
 Flat Ends 
 
 
 13430 12270 J11310 10520 
 
 9760 
 
 9040 8370 
 
 7920 
 
 6*5 
 
 Hinged Ends... 
 
 
 12900|11650 10620 
 
 9770 
 
 8960 
 
 8160 7430 6840 
 
 rr ** 
 
 d = 3-9 
 
 Round Ends . . . 
 
 * * * * ] 
 
 12170J 10750 9530 
 
 8490 
 
 7530 
 
 6670 5880 
 
 52130 
 
 
 
 
 1.46 
 
 1.95 
 
 2.43 
 
 2.91 
 
 3.40 
 
 3.88 4.37 
 
 4.85 
 
 7 "Light 
 
 Fixed Ends 
 
 
 13430 
 
 12270 
 
 11310 
 
 KMSfl 
 
 9680 
 
 RQfifi aan 
 
 7Qnn 
 
 
 Flat Ends 
 
 
 13430 12270 11310 10430 
 
 9680' 89(50 8320 7870 
 
 r = 2 64 
 J) tf i 
 
 Hinged Ends. . . 
 
 
 12900 1 11650 10620 9680 
 
 8870 8080 7370 6780 
 
 
 Round Ends 
 
 
 14170 10750 9530 8370 
 
 7430 6580 5810 5160 
 
 3=5 
 
 
 
 1.321 1.76 2.20 2.64 
 
 3.03 3.52, 3.96 4.40 
 
 6"He'vy 
 
 Fixed Ends 
 
 14380 
 
 12900 
 
 11670 
 
 10770 
 
 9920 
 
 9110 
 
 8370 
 
 7860 
 
 7410 
 
 r = 2 36 
 
 Flat Ends 14380 12900 11670 10770, 9920 
 
 9110 8370 
 
 7830 7*30 
 
 D5-8 
 __ m 
 
 Hinged Ends... 13940 12320 11010il0040i 9140 
 
 8250 7430 
 
 6720 6100 
 
 d 3-3 
 
 Round Ends ... 13330 11520 10020 8820 7720 
 
 6760 5880 
 
 5100 
 
 4440 
 
 
 
 1.14 
 
 1.70 
 
 2.27 
 
 2.84 3.41 
 
 3.98 
 
 4.54 
 
 5.11 
 
 5.68 
 
 6 "Light 
 
 Fixed Ends 
 
 14240 
 
 12900 
 
 11580 
 
 10690 
 
 9760 
 
 8880 
 
 8180 
 
 7720 
 
 7240 
 
 r = 2-27 
 
 Flat Ends 
 
 1 W40 
 
 129001158010690 
 
 9760 8880 ' 817'0 
 
 7680 
 
 7080 
 
 D=5. 3 
 
 d = 3-5 
 
 Hinged Ends... 13790 
 Round Ends ...j 13160 
 
 12320 10910| 9950 
 11520 9900 8710 
 
 89601 8000 7170 
 7530 6490 5490 
 
 6530 
 4890 
 
 58(50 
 4210 
 
 
 
 .90 
 
 1.351 1.80 
 
 2.25 
 
 2.70 
 
 3.15 3.60 
 
 4.05 
 
 4.50 
 
 5"He'vy 
 
 Fixed Ends 
 
 13700 
 
 12140 10860 
 
 9840 
 
 8800 
 
 8090 
 
 7500 
 
 6990 
 
 6490 
 
 r = 1 93 
 
 Flat Ends 
 
 13700 12140 10860 9840 8800 
 
 8070 
 
 7450 
 
 6720 
 
 6070 
 
 D4-9 
 
 Hinged Ends... 132001151010130 9050J 7910 
 
 7040 6220 
 
 5600 
 
 4S60 
 
 = 
 d = 2-5 
 
 Round Ends... 1250010600 89: J ,0 7630] 6400 
 
 5350 4560 
 
 3870 
 
 3240 
 
 
 
 1.16 
 
 1.74 
 
 2.32 2.90 3.48 
 
 4.06 
 
 4.64 
 
 5.22 
 
 5.80 
 
TABLE OF STRUTS. 
 
 147 
 
 No. 13. 
 LATTICED CHANNEL STRUTS. 
 
 GEEATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION, 
 
 USING FACTORS OF SAFETY GIVEN IN PREVIOUS TABLES. 
 
 The channels must be connected so as to 
 insure unity of action and separated not 
 less than the distances D or d respectively, 
 given in inches in the marginal columns. 
 Figures in heavy type under each length 
 represent the greatest distances apart in 
 feet on each channel that centres of lateral 
 bracing should be placed. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 SIZE 
 
 
 
 
 
 
 
 
 
 
 OF 
 
 OP 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 ENDS. 
 
 CHANNEL 
 
 8140 
 
 7770 
 
 7410 
 
 7070 
 
 6750 
 
 6440 
 
 6090 
 
 5750 
 
 5430 
 
 Fixed Ends... 
 
 8"He'vy 
 
 8120 
 
 7730 
 
 7330 
 
 6840 6370 
 
 6020 
 
 5650 
 
 5280 
 
 4880 Flat Ends 
 
 r = s-06 
 
 7100 
 
 6590 
 
 6100 
 
 5620 
 
 5170 
 
 4820 
 
 4440 4060 
 
 3620 Hinged Ends... 
 
 7.3 
 
 5420 
 
 4960 
 
 4440 
 
 3980 
 
 3540 
 
 3200 
 
 2820 2470 
 
 2150 Round Ends . . . 
 
 
 
 d ==. 4 . g 
 
 5.10 
 
 5.57 
 
 6.03 
 
 6.50 
 
 6.96 
 
 7.42 
 
 7.89 8.35 
 
 8.82 
 
 
 
 8140 
 
 7810 
 
 7450 
 
 7110 
 
 6790 
 
 6490 
 
 6130 
 
 5800 
 
 5510 
 
 Fixed Ends... 
 
 8 "Light. 
 
 8120 
 
 7780 
 
 7390 
 
 6900 
 
 6430 
 
 6070 
 
 5700 
 
 5340 
 
 4980 Flat Ends 
 
 r =^ 3 09 
 
 7100 
 
 6650 
 
 6160 
 
 5680 
 
 5220 
 
 48<iO 
 
 4480 
 
 4120 
 
 3730 Hinged Ends... 
 
 D7 1 
 
 5420 
 
 5030 
 
 4500 
 
 4030 
 
 3600 
 
 3240 
 
 2870 
 
 2510 2230 Round Ends... 
 
 ==i ' * 
 d ^ 5 .Q 
 
 4.27 
 
 7540 
 
 4.66 
 
 7190 
 
 5.04 
 
 6S30 
 
 5.43 
 
 6440 
 
 5.82 
 
 6050 
 
 6.21 
 
 5670 
 
 6.60 
 
 5310 
 
 6.99 7.38 
 4950 4570 
 
 Fixed Ends .. 
 
 7"He'vy 
 
 7500 
 
 7020 
 
 6490 
 
 6d20 
 
 5610 
 
 5180 
 
 4730 
 
 4300 
 
 3920! Flat Ends 
 
 
 6280 
 
 5800 
 
 5-280 
 
 4820 
 
 4390 
 
 3950 
 
 3460 
 
 3010 
 
 2640 Hinged Knds... 
 
 e-5 
 
 4630 
 
 4150 
 
 3650 
 
 3200 
 
 2^0 
 
 239< 
 
 2040 
 
 1730 
 
 153d Round Ends ... 
 
 v 
 
 d = 3.9 
 
 5.34 
 
 5.82 
 
 6.31 
 
 6.79 
 
 7.28 
 
 7.76 
 
 8.25 
 
 8.73 9.22 
 
 
 
 7500 
 
 7110 
 
 6750 
 
 6350 
 
 5960 
 
 5500 
 
 5190 
 
 4820 
 
 4450 
 
 Fixed Ends... 
 
 7 ' 'Light. 
 
 7450 
 
 6900 
 
 6370 5930! 5520 
 
 5C8( 
 
 4590 4170 
 
 3790 Flat Ends 
 
 
 6220 
 
 5680 
 
 5170 
 
 4720 4300 
 
 3840 
 
 3310 2890 
 
 2520 Hinged Ends... 
 
 D 1 
 
 4560 
 
 4030 
 
 3540 
 
 3100 2690 
 
 2310 
 
 1940 
 
 1660 
 
 1460 Round Ends . . . 
 
 w L 
 
 d ==J 4 2 
 
 4.84 
 
 5.28 
 
 5.72 
 
 6.16 6.59 
 
 7.03 
 
 7.47 
 
 7.91 
 
 8.35 
 
 
 
 6990 
 
 6580 
 
 6130 
 
 5710 5270 
 
 4870 
 
 4450 
 
 4060 
 
 3730 
 
 Fixed Ends... 
 
 6 ' ' He'vy 
 
 6720| 6160 
 
 5700 
 
 5230 
 
 4680 
 
 4220 
 
 3790 
 
 3400 
 
 3100 Flat Ends 
 
 r = 2*36 
 
 5500 
 
 4960 
 
 4480 
 
 4010 
 
 3410 
 
 2930 
 
 2520 
 
 2180 
 
 1950 Hinged Ends... 
 
 5. g 
 
 3870 
 
 3340 
 
 2870 
 
 2430 
 
 2010 
 
 1690 
 
 1460 
 
 12tlO 
 
 1100 Round Ends... 
 
 
 d = 3,3 
 
 6.25 
 
 6.82 
 
 7.38 
 
 7.95 
 
 8.52 
 
 9.C9 
 
 9.66 
 
 10.2210.79 
 
 
 
 6830 
 
 6350 
 
 5920 
 
 5470 
 
 5030 
 
 4610 
 
 4170 
 
 3830 
 
 3460 
 
 Fixed Ends... 
 
 6 "Light. 
 
 64 ;0 
 
 5280 
 
 5930 5470 
 47-20 4250 
 
 4931 
 3680 
 
 4390 
 3110 
 
 3960 
 
 26HO 
 
 3500 
 2250 
 
 3190 
 2020 
 
 2870 Flat Ends 
 1770 Hinged Ends... 
 
 i = 2 -27 
 D6 * 3 
 
 3650 
 
 3100 
 
 2640 
 
 2190 
 
 1790 1550 
 
 1310 
 
 1150 
 
 980, Round Ends . . 
 
 * 
 d S-6 
 
 4.95 
 
 5.40 
 
 5.85 
 
 6.30 
 
 6.75 7.20 
 
 7.65 
 
 8.10 
 
 8.55 
 
 
 
 5920 
 
 5430 
 
 4910 
 
 4410 
 
 3930 
 
 3530 
 
 3150 
 
 2780 
 
 2500 i Fixed Ends... 
 
 5"He'vy 
 
 5470 
 
 4880 
 
 4260 
 
 3750 
 
 3280 
 
 29-.'( 
 
 2640 
 
 2360 
 
 2140 Flat Ends 
 
 r =-- i * 93 
 
 4250 
 
 362* ) 
 
 2970 
 
 2480 
 
 2080 
 
 1820 
 
 1570 
 
 1340 
 
 1180 Hinged Ends... 
 
 D4 . 9 
 * v 
 
 2640 
 
 2150 
 
 1710 
 
 1440 
 
 1190 
 
 1010 
 
 880 
 
 760 
 
 670 Round Ends . . . 
 
 d = 3.5 
 
 6.38 
 
 6.96 
 
 7.54 
 
 8.12 
 
 8.70 
 
 9.28 
 
 9.86 
 
 10.44 
 
 11.02 
 
 
 
148 
 
 TABLE OF STRUTS. 
 
 No. 14. 
 LATTICED CHANNEL STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION, 
 USING FACTORS OF SAFETY GIVEN IN PREVIOUS TABLES, g 
 
 For a pair of braced channel? or for a single channel secured from \ ( \- * 
 flexure in the direction of the flanges and liable to fail only in the 
 direction of the web C D. jf-jrl"jB 
 
 r in tlie marginal columns gives the radius of gyration for axis 
 A B, or for either axis of the combined pair of channels. See de- h 
 scrip lion, page 121. L r^ 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OP 
 
 OP 
 
 
 
 
 
 
 
 
 
 
 CHANNEL. 
 
 ENDS. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 *_ 
 
 .*_ 
 
 16 
 
 18 
 
 5" 
 
 Fixed Ends 
 
 
 13570 
 
 12010 
 
 10770 
 
 9680 
 
 8650 
 
 8000 
 
 7410 
 
 6870 
 
 Light .... 
 
 Flat Ends 
 
 
 1357012010 
 
 10770 9680 
 
 8G50 
 
 7970 
 
 733H 
 
 6550 
 
 r = i-ws 
 
 Hinged Ends. .. 
 
 ..'.'.'. 
 
 13050 11380 
 
 10040 8870 
 
 7750 
 
 6910 
 
 6100 5340 
 
 D= 4 ' 5 
 
 Round Ends 
 
 
 12330 10440 
 
 8820 7430 
 
 6220 
 
 5200 
 
 4440 3710 
 
 d = 2-8 
 
 
 
 .96 
 
 1.13 
 
 1.91 
 
 2.39 
 
 2.87 
 
 3.35 
 
 3.83 4.31 
 
 4" 
 
 Fixed Ends . 
 
 
 12900 
 
 11220 
 
 9840 
 
 8650 
 
 7810 
 
 7150 
 
 6490 
 
 5840 
 
 Heavy. 
 
 Flat Ends 
 
 
 129011 
 
 11220 
 
 9840 
 
 8650 
 
 7780 
 
 6960 6070 5380 
 
 r = 1 55 
 
 Hiuged Ends 
 
 
 12320 
 
 10520 
 
 9050 
 
 7750 
 
 650 
 
 5740 4860 4160 
 
 D = 4 ' 
 
 Round Ends. 
 
 
 11520 
 
 9410 
 
 7630 
 
 6220 
 
 5030 
 
 4090 3240 2550 
 
 d = 1-9 
 
 
 
 1.29 
 
 1.94 
 
 2.53 
 
 3.23 
 
 3.88 
 
 4.52 5.17 
 
 5.81 
 
 4" 
 
 Fixed Ends 
 
 
 12900 
 
 11130 
 
 9840 
 
 8580 
 
 7810 
 
 7110 
 
 t!440 
 
 5800 
 
 Light . . 
 
 Flat Ends 
 
 
 12900 
 
 11130 
 
 0840 
 
 85SO 
 
 7780 
 
 6900 
 
 6020 5340 
 
 r&= ^sV 
 D= 3-8 
 
 Hinged Ends 
 
 
 12320 
 11520 
 
 10420 9050 7670 
 9290' 7630 6130 
 
 6650 
 5030 
 
 5680 4820 4120 
 4030 i aannl asm 
 
 Round Euds 
 
 
 d = 2 
 
 
 
 
 1.25 
 
 1.87 2.50 3.12 
 
 3.74 
 
 4.37 
 
 4.99 5.62 
 
 3" 
 
 Fixed Ends 
 
 14240 
 
 11670 
 
 9840 8280 7370 
 
 6490 
 
 5590 
 
 4780 
 
 3960 
 
 
 Flat EIKIS 
 
 14240 
 
 11670 
 
 9840 
 
 8270 ! 7270 6070 
 
 5080 
 
 4130 
 
 3310 
 
 r = 1-18 
 
 Hinged Ends... 
 
 13790 
 
 11010 
 
 9050 
 
 7300 6040 i 4860 
 
 3840 
 
 2850 
 
 2110 
 
 D=3-l 
 
 Round Ends. .. 
 
 13160 
 
 10020 
 
 7630 
 
 5730 
 
 43801 3240; 2310 
 
 1640 
 
 1210 
 
 d = 1-1 
 
 
 .79 
 
 1.59 
 
 2.38 
 
 3.18 
 
 3.97 
 
 4.36 
 
 4.76 
 
 5.15 
 
 5.55 
 
 H" 
 
 Fixed Ends.... 
 
 13300 
 
 ias4o 
 
 8180 
 
 6950 
 
 5750 
 
 4610 
 
 3560 
 
 2730 
 
 2090 
 
 
 Flat Ends 
 
 13300 
 
 10340 
 
 8170 
 
 6660 
 
 5280 1 39601 2950 
 
 28801 1840 
 
 r = -85 
 
 Hinged Ends... 
 
 12760 
 
 9590 
 
 7170 
 
 5450 
 
 4060 2580 
 
 1840 
 
 1310 
 
 1000 
 
 D = 2-4 
 
 Round Ends... 
 
 12000 
 
 8260 
 
 5490 
 
 3810 
 
 2470 
 
 1550 
 
 1030 
 
 740 
 
 580 
 
 d = -54 
 
 
 1.01 
 
 2.02 
 
 3.03 
 
 4.05 
 
 5.06 
 
 6.07 7.08 
 
 8.10 
 
 9.11 
 
 2" 
 
 Fixed Ends 
 
 12780 
 
 9590 
 
 7630 
 
 6220 
 
 4910 
 
 3690 
 
 2710 
 
 1980 
 
 1580 
 
 
 Flat Ends 
 
 12780 
 
 9590 
 
 7590 
 
 5790 
 
 4260 
 
 3070 
 
 2300 
 
 1760 
 
 1300 
 
 r = -74 
 
 Hinged Ends... 
 
 12190 
 
 8780 
 
 6410 
 
 4580 
 
 2970 
 
 1930 
 
 1300 
 
 950 
 
 710 
 
 D = 2-l 
 
 Round Ends... 
 
 11360 
 
 7330 
 
 47601 2960 
 
 1710 
 
 1090 
 
 740 
 
 550 
 
 400 
 
 d = -60 
 
 
 .84 
 
 1.68 
 
 2.52 
 
 3.35 
 
 4.19 
 
 5.03 
 
 5.87 
 
 6.70 
 
 7.54 
 
TABLE OF STRUTS. 
 
 149 
 
 No. 14. 
 LATTICED CHANNEL STRUTS. 
 
 GREATEST SAFE LOAD IX LBS. PER SQUARE INCH OF SECTION, 
 USING FACTORS OF SAFETY GIVEN IN PREVIOUS TABLES. 
 
 The channels must be connoted so as to 
 insure unity of action and separated not 
 less than the distances I) or d respectively, 
 
 fiven in inches in the marginal columns. . 
 'igures in heavy type under each length 
 represent the greatest distances apart in 
 feet on each channel that centres of lateral 
 bracing should be placed. 
 
 LENGTH IN FEET. 
 
 
 
 
 CONDITION 
 
 SIZE 
 
 
 
 
 
 
 
 
 
 
 OP 
 
 OP 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 ENDS. 
 
 CHANNEL. 
 
 6310 
 
 5800 
 
 5270 4740 
 
 4210 
 
 3790 
 
 ,3370 
 
 2970 
 
 2640 
 
 Fixed Ends 
 
 5" 
 
 5880 
 
 5340 
 
 46801 4090 
 
 3540 
 
 3160 
 
 2800 
 
 2500 
 
 2250 
 
 Flat Ends 
 
 Light. 
 
 4670 
 
 4120 
 
 3410i 2800 
 
 2280 
 
 1990 
 
 1710 
 
 1450 
 
 1260 
 
 Hinged Ends. .. 
 
 r = 1-88 
 
 3050 
 
 2510 
 
 2010 
 
 1620 
 
 1330 
 
 1130 
 
 950 
 
 820 
 
 720 
 
 Round Ends 
 
 D = 4 ' 5 
 
 4.78 
 
 5.26 
 
 5.74 
 
 6.22 
 
 6.70 
 
 7.18 
 
 7.66 
 
 8.14 
 
 8.61 
 
 
 d = 2-8 
 
 5190 
 
 4570 
 
 3960 
 
 3460 
 
 2970 
 
 2590 
 
 2240 
 
 1920 
 
 1740 
 
 Fixed Ends... 
 
 4" 
 
 4590 
 
 3920 
 
 ,3310 
 
 2870 
 
 2500 
 
 2210 
 
 1950 
 
 1700 
 
 1490 
 
 Flat Ends 
 
 Heavy. 
 
 3310 
 1940 
 
 2640 
 1530 
 
 2110 
 1210 
 
 1770 
 980 
 
 1450 1230 
 820 700 
 
 1070 
 610 
 
 910 
 530 
 
 800 
 450 
 
 Hinged Ends... 
 Round Ends 
 
 r =-- 1 66 
 
 6.46 
 
 7.10 
 
 7.75 
 
 8.39 
 
 9.04 
 
 9.68 
 
 10.32 
 
 10.97 
 
 11.61 
 
 
 d = 1-9 
 
 5150 
 
 4490 
 
 3930 
 
 3400 
 
 2940 
 
 2540 
 
 2200 
 
 1900 
 
 1700 
 
 Fixed Ends... 
 
 4" 
 
 4540 
 32fiO 
 
 3830 
 
 25ti() 
 
 3280 
 
 2080 
 
 2830 
 1730 
 
 2480 
 1430 
 
 2170 
 1210 
 
 1920 
 1050 
 
 1680 
 900 
 
 1440 Flat Ends 
 780|HineedEnds... 
 
 WM 
 
 1900 
 
 14-0 
 
 1190 
 
 960 
 
 810 
 
 690 
 
 600 
 
 520 
 
 430 
 
 Round Ends 
 
 D = 3-8 
 
 6.24 
 
 6.86 
 
 7.48 
 
 8.11 
 
 8.73 
 
 9.35 
 
 9.97 
 
 10.60 
 
 11.22 
 
 
 d = 2-0 
 
 3280 
 
 2680 
 
 2220 
 
 1850 
 
 1610 
 
 1390 
 
 1180 
 
 1020 
 
 900 
 
 Fixed Ends... 
 
 3" 
 
 2730 
 
 2280 
 
 1940 
 
 1620 
 
 1330 
 
 1080 
 
 870 
 
 700 
 
 560 Flat Ends 
 
 
 1650 
 
 1280 
 
 1060 
 
 870 
 
 730 
 
 620 
 
 530 
 
 440 
 
 370 Hinged Ends... 
 
 r = 1-18 
 
 920! 730! 610 
 
 500 
 
 410 
 
 350 
 
 280 
 
 230 
 
 200; Round Ends ... 
 
 D=3-l 
 
 7.94 
 
 8.33 
 
 8.72 
 
 9.12 
 
 9.51 
 
 11.90 
 
 12.29 
 
 12.69 
 
 13.08 
 
 
 d = 1-1 
 
 1690 
 1430 
 
 1380 
 106U 
 
 1100 
 
 800 
 
 930 
 
 600 
 
 770 
 450 
 
 
 
 
 
 Fixed Ends.... 
 Flat Ends... 
 
 2V 
 
 
 
 
 
 
 770 
 
 610 
 
 490 
 
 390 
 
 5>90 
 
 
 
 
 . Hinged Ends... 
 
 r = -85 
 
 430 
 
 340 
 
 260 
 
 210 170 
 
 
 
 
 
 Round Ends. 
 
 D = 2-4 
 
 10.12 
 
 11 13 
 
 12 14 13 Ifi 14 17 
 
 
 
 
 
 
 d = -64 
 
 1250 
 
 990 
 
 800 
 
 
 
 
 
 
 
 FiTod "Ends 
 
 2" 
 
 930 
 
 670 
 
 470 
 
 
 
 
 
 
 Flat Ends 
 
 
 560 
 
 420 
 
 310 
 
 
 
 
 
 
 Hinged Ends... 
 
 r = -74 
 
 300 
 
 230 
 
 180 
 
 
 
 
 
 Round Ends. 
 
 T) = 2 " * 
 
 8.38 
 
 9.22 
 
 10.05 
 
 
 
 
 
 
 
 d = 80 
 
 
 
 
 
 
 
150 TABLES OF STRUTS. 
 
 No. 15. 
 PENCOYD CHANNELS AS STRUTS. 
 
 GREATEST SAFE LOADS IN LBS. PER SQ. INCH OF SECTION, WHEN THE 
 STRUTS ARE FREE TO BEND AT RIGHT ANGLES TO THE WEB OR IN 
 THE WEAKEST DIRECTION, USISG FACTORS OF SAFETY GIVEN IN 
 PREVIOUS TABLES. 
 
 SIZE 
 
 OP 
 
 CHANNEL 
 
 CONDITION 
 
 OF 
 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 1 V 
 
 Fixed Ends.... 
 
 14240 
 
 11580 
 
 9680 
 
 8180 
 
 7240 
 
 6350 
 
 5430 
 
 4570 
 
 3790 
 
 S-O 
 
 Flat Ends 
 
 14240 
 
 11580 9680 
 
 8170 
 
 7080 
 
 5930 
 
 4880 
 
 3920 
 
 3160 
 
 
 Hinged Ends.. . 
 
 13790 
 
 10910 8870 
 
 7170 
 
 5S60 
 
 4720 
 
 3620 
 
 2640 
 
 1990 
 
 T = 1-13 
 
 Round Ends 
 
 13160 
 
 9900 
 
 7430 5490 
 
 4210 
 
 3100 
 
 2150 
 
 1530 
 
 1130 
 
 1 0" 
 
 Fixed Ends 
 
 13570 
 
 10690 
 
 8580 7320 
 
 6220 
 
 5110 
 
 4060 
 
 3220 
 
 2520 
 
 LA 
 
 Flat Ends 
 
 13570 
 
 10690 
 
 8580 7210 5790 
 
 4490 
 
 3400 
 
 2690 
 
 2160 
 
 Heavy 
 
 I = -92 
 
 Hinged Ends... 
 Round Ends 
 
 13050 
 12330 
 
 9950 
 8710 
 
 7670 5980 4580 
 6130 4320 2960 
 
 3210 
 4860 
 
 2180 
 1260 
 
 1610 
 900 
 
 1200 
 680 
 
 10" 
 
 Fixed Ends... 
 
 12780 
 
 9590 
 
 7630 6220 4910 
 
 3660 
 
 2710 
 
 1980 
 
 1580 
 
 1 
 
 Flat Ends 12780 
 
 9590 
 
 7590 5790 4260 
 
 3040 
 
 2300 
 
 1760 
 
 1300 
 
 Light 
 
 I = -74 
 
 Hinged Ends... 
 Round Ends. . . . 
 
 12190 
 11360 
 
 8750 
 7330 
 
 6410 
 4760 
 
 4580 
 2960 
 
 2970 
 1710 
 
 1910 
 1070 
 
 1300 
 740 
 
 950 
 550 
 
 710 
 400 
 
 1 0" 
 
 Fixed Ends... 
 
 13160 
 
 10260 
 
 8140 
 
 6910 
 
 5670 
 
 4530 
 
 3500 
 
 2660 
 
 2020 
 
 1U 
 
 Flat Ends 
 
 13160 
 
 10260 
 
 8120 
 
 6600 
 
 5180! 3870 
 
 2900 
 
 2260 
 
 1790 
 
 Heavy. . . . 
 
 Hinged Ends... 
 
 12610 
 
 9500 
 
 7100 
 
 5390 
 
 3950' 2600 
 
 1800 
 
 1270 
 
 970 
 
 r = -84 
 
 Round End*. . . . 
 
 11840 
 
 8150 
 
 5420 
 
 3760 
 
 2390 
 
 1500 
 
 1000 
 
 720 
 
 560 
 
 10" 
 
 Fixed Ends 
 
 12400 
 
 9190 
 
 7320 
 
 5840 
 
 4410 
 
 3220 
 
 2340 
 
 1740 
 
 1360 
 
 1U 
 
 Flat Ends 1->400 
 
 9190 
 
 7210 
 
 5380 
 
 3750 2690 
 
 2020 
 
 1490 
 
 1040 
 
 Light 
 
 r = -69 
 
 Hinged Ends... 
 Round Ends 
 
 11780 
 10900 
 
 8330 
 6850 
 
 5980 
 4320 
 
 4160 
 2550 
 
 2480 
 1440 
 
 1610 
 900 
 
 1110 
 630 
 
 800 
 450 
 
 600 
 340 
 
 Q" 
 
 Fixed Ends 
 
 12400 
 
 9110 
 
 7240 
 
 5750 
 
 4330 
 
 3120 
 
 2240 
 
 1690 
 
 1320 
 
 y 
 
 Flat Ends ! 12400 
 
 9110 
 
 7080 
 
 5280 
 
 3K60 
 
 2620 
 
 1950 
 
 1430 1000 
 
 Heavy 
 
 Hinged Ends... 
 
 11780 
 
 8250 
 
 5860 
 
 4060 
 
 2400 
 
 1550 
 
 1U70 
 
 7',0| 590 
 
 r -= -6S 
 
 Round Ends 
 
 10900 
 
 6760 
 
 4210 
 
 2470 
 
 1390 
 
 870 
 
 610 
 
 430 
 
 320 
 
 Q" 
 
 Fixed Ends 
 
 11670 
 
 8370 
 
 6620 
 
 4910 
 
 3400 
 
 2310 
 
 1660 
 
 1240 
 
 940 
 
 V 
 
 Flat Ends 
 
 11670 
 
 8370 
 
 081*. 
 
 4260 
 
 2830 
 
 2000 
 
 1390 
 
 920 
 
 600 
 
 Light 
 
 Hinged Ends... 
 
 11010 
 
 74:30 
 
 5010 
 
 2970 
 
 1731 
 
 1100 
 
 760 
 
 560 
 
 390 
 
 r= -6 
 
 Round Ends 
 
 10080 
 
 5880 
 
 3390 
 
 1710 
 
 960 
 
 630 
 
 420 
 
 300 
 
 210 
 
TABLES OF STKUTS. 
 
 151 
 
 No. 15. 
 
 PENCOYD CHANNELS AS STRUTS. 
 
 T. JU 
 
 r in marginal columns is the radius of gyration taken around axis A B. 
 When strut is hinged the pins are supposed to lie in the direction A B. 
 When the pins are in the direction (J D, consider the strut flat ended by 
 tliis table. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 OP 
 
 ENDS. 
 
 SIZE 
 
 OF 
 
 CHANNEL. 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 6 
 
 3120 
 26211 
 1550 
 870 
 
 1940 
 1730 
 930 
 540 
 
 1250 
 930 
 560 
 300 
 
 1650 
 1380 
 750 
 420 
 
 1050 
 73f 
 450 
 240 
 
 1020 
 690 
 440 
 230 
 
 710 
 400 
 260 
 160 
 
 2540 
 2170 
 1210 
 690 
 
 1640 
 1360 
 740 
 410 
 
 990 
 670 
 420 
 230 
 
 1350 
 1030 
 600 
 330 
 
 830 
 490 
 330 
 190 
 
 810 
 470 
 310 
 180 
 
 2070 
 1830 
 990 
 570 
 
 1360 
 1040 
 600 
 340 
 
 800 
 470 
 310 
 180 
 
 1070 
 770 
 470 
 250 
 
 670 
 370 
 240 
 150 
 
 1760 
 1520 
 820 
 460 
 
 1100 
 800 
 490 
 260 
 
 1520 
 1220 
 680 
 370 
 
 950 
 610 
 400 
 210 
 
 1300 
 980 
 580 
 320 
 
 790 
 4fiO 
 300 
 170 
 
 1090 
 800 
 490 
 260 
 
 970 
 640 
 410 
 220 
 
 840 
 500 
 330 
 190 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends. .. 
 Round Ends . . . 
 
 Fixed End? 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends.... 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends. .. 
 Round Ends.... 
 
 Fixed Ends 
 Flat Ends. . .. 
 Hinged Ends... 
 Round Ends 
 
 15" 
 
 r = 1-13 
 
 12" 
 
 Heavy. 
 
 12" 
 
 Light. 
 
 r -74 
 
 10" 
 
 Heavy. 
 10" 
 
 r W;, 
 9" 
 
 Heavy. 
 
 r -68 
 
 9" 
 
 Light. 
 
 r~ - '60 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 910 
 
 570 
 370 
 200 
 
 740 
 430 
 280 
 170 
 
 
 
 
 
 
 
 
 l 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 [::::: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
152 TABLES OF STRUTS. 
 
 No. 16. 
 PENCOYD CHANNELS AS STRUTS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQ. INCH OF SECTION WHEN THE 
 STRUTS ARE FKEE TO BEND AT RIGHT ANGLES TO THE WEB OR 
 IN THE WEAKEST DIRECTION, USING FACTORS OF SAFETY GIVEN 
 IN PREVIOUS TABLES. 
 
 SIZE 
 
 OF 
 
 CHANNEL 
 
 CONDITION 
 
 OF 
 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 Q" 
 
 Fixed Ends... 
 
 12520 
 
 9350 
 
 7450 
 
 6010 
 
 4610 
 
 3400 
 
 2470 
 
 1840 
 
 1450 
 
 o 
 
 Flat Ends 
 
 12520! 9350 
 
 7390 
 
 5.560 
 
 3960 
 
 2830 
 
 2120 
 
 1610 
 
 1150 
 
 Heavy. . . 
 
 Hinged Ends. .. 
 
 11920: 8510 
 
 6160 
 
 4350 
 
 2680 
 
 1730 
 
 1170 
 
 870 
 
 650 
 
 r = -71 
 
 Round Ends . . . 
 
 11060 
 
 7040 
 
 4500 
 
 273U 
 
 1550 
 
 960 
 
 670 
 
 50C 
 
 360 
 
 Q" 
 
 Fixed Ends 
 
 11760 
 
 8420 
 
 6670 
 
 5000 
 
 3500 
 
 2410 
 
 1720 
 
 1290 
 
 980 
 
 O 
 
 Flat Ends 
 
 117'60 
 
 8420 
 
 6260 
 
 4350 
 
 2900 
 
 2070 
 
 1460 
 
 970 
 
 650 
 
 Light.... 
 
 r = -60 
 
 Hinged Ends... 
 Uoinul Ends . . . 
 
 11110 
 10140 
 
 7500 
 5950 
 
 5060 
 3440 
 
 3069 
 1760 
 
 1800 
 1000 
 
 1140 
 650 
 
 790 
 440 
 
 580 
 320 
 
 420 
 230 
 
 7" 
 
 Fixed Ends 
 
 12140 
 
 8880 
 
 7030 
 
 5470 
 
 4000 
 
 2830 
 
 2000 
 
 1550 
 
 1170 
 
 I 
 
 Flat Ends 
 
 12140 
 
 8880 
 
 6780 
 
 4930 
 
 3340 
 
 2400 
 
 J780 
 
 1260 
 
 860 
 
 Heavy 
 
 Hinged Ends... 
 
 11510 
 
 8000 
 
 5560 
 
 3680 
 
 2130 
 
 1370 
 
 960 
 
 700 
 
 530 
 
 r = -66 
 
 Round Ends 
 
 10600 
 
 6490 
 
 3920 
 
 2190 
 
 1230 
 
 770 
 
 560 
 
 . 390 
 
 280 
 
 7" 
 
 Fixed Ends.... 
 
 11670 
 
 8280 
 
 6490 
 
 4780 
 
 3280 
 
 2220 
 
 1610 
 
 1180 
 
 900 
 
 i 
 
 Flat Ends 
 
 11670| 8270 
 
 6070 
 
 4130 
 
 2730 
 
 1940 
 
 1330 
 
 870 
 
 560 
 
 Light 
 
 [linged Ends. .. 
 
 11010 
 
 7300 
 
 4860 
 
 2850 
 
 1650 
 
 1060 
 
 730 
 
 530 
 
 370 
 
 r = -5S 
 
 Round Ends . . . 
 
 10020 
 
 5730 
 
 3240 
 
 1640 
 
 920 
 
 610 
 
 410 
 
 280 
 
 200 
 
 fi" 
 
 ?ixed Ends 
 
 12270 
 
 9040 
 
 7190 
 
 5670 
 
 4210 
 
 3030 
 
 2150 
 
 1640 
 
 1270 
 
 u 
 
 ?lat Ends 
 
 12270 
 
 9040 
 
 7020 
 
 5180 
 
 3540 
 
 2550 
 
 1890 
 
 1360 
 
 950 
 
 Heavy 
 
 linged Ends... 
 
 11650 
 
 8160 
 
 5800 
 
 3! 50 
 
 2280 
 
 1490 
 
 1030 
 
 740 
 
 570 
 
 r = -7 
 
 lound Ends . . . 
 
 10750 
 
 6670 
 
 4150 
 
 2390 
 
 1330 
 
 840 
 
 590 
 
 410 
 
 310 
 
 fi" 
 
 Hxed Ends. .. 
 
 11130 
 
 7770 
 
 5750 
 
 3890 
 
 2520 
 
 1690 
 
 1200 870 
 
 
 Flat Ends. 
 
 11130 
 
 7730 
 
 5280 
 
 3250 
 
 2160 
 
 1430 
 
 880 
 
 530 
 
 
 Light.... 
 
 r -= -51 
 
 Hinged Ends... 
 Round Ends . . . 
 
 10420 
 9290 
 
 6590 
 4960 
 
 401)0 
 2470 
 
 2060 
 1180 
 
 1-200 
 680 
 
 770 
 4:30 
 
 540 
 290 
 
 350 
 200 
 
 
 K" 
 
 Fixed Ends... 
 
 11490 
 
 8140 
 
 6260 
 
 4530 
 
 3060 
 
 2020 
 
 1500 
 
 1070 
 
 820 
 
 u 
 
 Flat Ends 
 
 114K) 
 
 8120 
 
 5830 
 
 3870 
 
 2570 
 
 1790 
 
 1200 
 
 770 
 
 480 
 
 Heavy 
 
 Hinged Ends... 
 
 10820 
 
 7100 
 
 4620 
 
 2600 
 
 1510 
 
 970 
 
 670 
 
 470 
 
 320 
 
 r = -5 
 
 Round Ends . . . 
 
 9780 
 
 5420 
 
 3000 
 
 1500 
 
 850 
 
 560 
 
 370 
 
 250 
 
 180 
 
TABLES OF STRUTS. 
 
 No. 16. 
 PENCOYD CHANNELS AS STRUTS. 
 
 153 
 
 r, in marginal columns, is the radius of gyration taken around axis A B. 
 When strut is hinged, the pins are supposed to lie in the direction A B. 
 When the pins are in the direction CD, consider the strut flat ended by this 
 tuble. 
 
 SIZE 
 
 CONDITION 
 
 LENGTH IN FEET. 
 
 OP 
 
 OP 
 
 
 
 
 
 
 
 
 
 
 CHANNEL 
 
 ENDS. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 K" 
 
 Fixed Ends 
 
 10600 
 
 7190 
 
 5000 
 
 3090 
 
 1870 
 
 1290 
 
 890 
 
 
 
 
 
 Flat Ends 10600 
 
 7020 
 
 4350 
 
 2600 
 
 1650 
 
 970 
 
 550 
 
 
 
 Light.... 
 
 r = -45 
 
 Hinged E.ids.. . 
 Round Ends . . . 
 
 9860 
 8(500 
 
 5800 
 4150 
 
 3060 
 1760 
 
 1530 
 860 
 
 890 
 510 
 
 580 
 320 
 
 3GO 
 200 
 
 
 
 
 
 A" 
 
 Fixed Ends ... 
 
 11040 
 
 7080 
 
 5630 
 
 3760 
 
 2410 
 
 1630 
 
 1130 
 
 830 
 
 
 rr 
 
 Flat Ends 
 
 11040 
 
 7640 
 
 5130 
 
 3130 
 
 2070 
 
 1350 
 
 8:30 
 
 490 
 
 
 Heavy. . . 
 
 Hinged Ends.. . 
 
 10330 
 
 6470 
 
 3900 
 
 1970 
 
 1140 
 
 740 
 
 510 
 
 320 
 
 
 r = -50 
 
 Round Ends . . . 
 
 9170 
 
 
 2350 
 
 1120 
 
 650 
 
 410 
 
 270 
 
 190 
 
 
 
 A" 
 
 Fixed Ends 
 
 10860 
 
 7500 
 
 5390 
 
 3500 
 
 2180 
 
 1500 
 
 1040 
 
 740 
 
 
 4: 
 
 Flat Ends 
 
 10860 
 
 7450 
 
 4830 
 
 2900 
 
 1910 
 
 1200 
 
 720 
 
 430 
 
 
 Light .... 
 
 Hinged Ends. . . 
 
 10130 
 
 6220 
 
 3570 
 
 1800 
 
 1040 
 
 670 
 
 450 
 
 280| 
 
 r = -4b 
 
 Round Ends . . . 
 
 8930 
 
 4560 
 
 2120 
 
 1000 
 
 600 
 
 370 
 
 240 
 
 170 
 
 
 
 0" 
 
 Fixed Ends 
 
 10690 
 
 7320 
 
 5110 
 
 3220 
 
 1940 
 
 1360 
 
 950 
 
 670 
 
 
 o 
 
 Flat Ends 
 
 10690 
 
 7210 
 
 4490 
 
 2690 
 
 1730 
 
 1040 
 
 610 
 
 370 
 
 
 
 Hinged Ends . . 
 
 9950 
 
 5980 
 
 3210 
 
 1610 
 
 930 
 
 600 
 
 400 
 
 240 
 
 '. '. '. '. '. 
 
 r = -46 
 
 Round Ends . . . 
 
 8710 
 
 4320 
 
 1860 
 
 900 
 
 540 
 
 340 
 
 220 
 
 150 
 
 
 
 91" 
 
 Fixed Ends 
 
 10340 
 
 6990 
 
 4690 
 
 2800 
 
 1730 
 
 1140 
 
 790 
 
 
 
 "4" 
 
 Flat Ends 
 
 10340 
 
 6720 
 
 4040 
 
 2380 
 
 1470 
 
 840 
 
 460 
 
 ... 
 
 
 
 Hinged Ends.. . 
 
 9590 
 
 5500 
 
 2760 
 
 1350 
 
 790 
 
 510 
 
 300 
 
 
 
 r = -43 
 
 Round Ends 
 
 8260 
 
 3870 
 
 1590 
 
 760 
 
 440 
 
 270 
 
 170 
 
 
 
 O" 
 
 Fixed Ends. 
 
 8650 
 
 5190 
 
 2'90 
 
 1390 
 
 810 
 
 
 
 
 
 2 
 
 Flat Ends 
 
 8650 
 
 4590 
 
 2210 
 
 1080 
 
 480 
 
 
 
 
 
 
 Hinged Ends ! . 
 
 7750 
 
 3310 
 
 1230 
 
 62*. 
 
 310 
 
 
 
 
 
 r = -31 
 
 Round Ends . . . 
 
 6220 
 
 1940 
 
 700 
 
 350 
 
 180 
 
 
 
 
 
 
 
 
 
154 TABLES OF STKUTS. 
 
 WROUGHT IRON COLUMNS OR PILLARS OF ROUND 
 AND SQUARE CROSS SECTION. 
 
 Experiments on columns of this class are not very complete, 
 especially as denoting the comparative values for the various end 
 conditions. The following tables, Nos. 17 and 18, are derived 
 partly from experiment on actual columns, extended and com- 
 pleted by comparison with the experiments on rolled struts 
 from which all our previous tables of strut resistances are derived. 
 
 Table No. 2 is taken as the basis for the working values. On 
 account of the more perfect symmetry of form possessed by round 
 and square sections than the shapes for which table No. 2 was 
 especially calculated, the safe loads per square inch of section 
 are increased ten (10) per cent, for round columns, and five (5) 
 per cent, for square columns. That is, the factors of safety pre- 
 viously given remaining the same, the ultimate strength is sup- 
 posed to be 10 and 5 per cent, respectively greater than the 
 rolled struts. 
 
 The tables are calculated for certain thicknesses of iron vary- 
 ing from " for 2" diameter up to " for 12" diameter, as 
 marked in the margins. At the same place R represents 
 the radius of gyration for the diameter and thickness given. 
 When the thickness varies but a little from that given, the 
 strength per square inch of section can be accepted as practically 
 unchanged. But when the variation becomes of importance, 
 the radius of gyration corresponding to the altered thickness 
 will have to be obtained, and the strength of the column then 
 ascertained from table No. 2, as heretofore described. 
 
 The following table gives the values of the radius of gyration 
 for round and square columns from 2 to 12 inches diameter, and 
 .from ^ of an inch to 1 inch thick. 
 
 Example for Round Column : 
 
 What is the greatest safe load for a flat-ended round column 
 6 inches outer diameter, |" thick, 8.64 sq. in. area, and 18 feet 
 
 long, r^l.95 - =111. By table No. 2 the corresponding 
 
 safe load = 6780 Ibs. + 10 per cent. = 7460 Ibs. per sq. inch of 
 section, or 64,440 Ibs. for the column. 
 
 For a square column add 5 per cent, to table No. 2, instead of 
 10 per cent, as above. 
 
TABLES OF STKUTS. 
 
 155 
 
 RADII OF GYRATION FOR ROUND COLUMNS. 
 
 
 THICKNESS IN INCHES VARYING BY TENTHS. 
 
 OUTSIDE 
 DIAMETER 
 
 
 .2 
 
 .3 
 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 1.0 
 
 OP COLUMN 
 
 
 
 
 
 
 
 
 
 
 
 IN INCHES. 
 
 CORRESPONDING RADIUS OP GYRATION IN INCHES. 
 
 2 
 
 .67 
 
 .64 
 
 .61 
 
 .58 
 
 .56 
 
 .54 
 
 .52 
 
 .51 
 
 .50 
 
 .50 
 
 3 
 
 1.03 
 
 .99 
 
 .96 
 
 .93 
 
 .90 
 
 .88 
 
 .85 
 
 .83 
 
 .81 
 
 .79 
 
 4 
 
 1.38 
 
 1.35 
 
 1.31 
 
 1.28 
 
 1.45 
 
 1.22 
 
 1.19 
 
 1.16 
 
 1.14 
 
 1.12 
 
 5 
 
 1.73 
 
 1.70 
 
 1.66 
 
 1.63 
 
 1.6D 
 
 1.57 
 
 1.54 
 
 1.51 
 
 1.48 
 
 1.46 
 
 6 
 
 2.08 
 
 2.05 
 
 2.02 
 
 1.98 
 
 1.95 
 
 1.92 
 
 1.89 
 
 1.86 
 
 1.83 
 
 1.80 
 
 7 
 
 2.43 
 
 2.40 
 
 2.36 
 
 2.33 
 
 2,30 
 
 2.27 
 
 2.24 
 
 2.21 . 
 
 2.18 
 
 2.15 
 
 8 
 
 2.79 
 
 2.76 
 
 2.72 
 
 2.69 
 
 2.66 
 
 2.62 
 
 2 59 
 
 2.56 
 
 2.53 
 
 2.50 
 
 9 
 
 3.15 
 
 3.11 
 
 3.08 
 
 3.04 
 
 3.01 
 
 2.97 
 
 2.94 
 
 2.91 
 
 2.882.85 
 
 10 
 
 3.51 
 
 3.47 
 
 3.44 
 
 3.40 
 
 3.37 
 
 3.33 
 
 3.3J 
 
 3.27 
 
 3.23 
 
 3.20 
 
 11 
 
 3.86 
 
 3.82 
 
 3.79 
 
 3.75 
 
 3.72 
 
 3.68 
 
 3.65 
 
 3.62 
 
 3.583.55 
 
 12 
 
 4.21 
 
 4.18 
 
 4.15 
 
 4.11 
 
 4.08 
 
 4.04 
 
 4.01 
 
 3.97 
 
 3.94 
 
 3.90 
 
 RADII OF GYRATION FOR SQUARE COLUMNS. 
 
 OUTER 
 
 THICKNESS IN INCHES VARYING BY TENTHS. 
 
 DIAMETER 
 
 
 
 
 
 
 
 
 
 
 
 ACROSS 
 
 .1 
 
 .2 
 
 3 
 
 .4 
 
 .5 
 
 .6 
 
 .7 
 
 .8 .9 
 
 1.0 
 
 FLATS IN 
 
 
 
 
 
 
 
 
 
 
 INCHES. 
 
 CORRESPONDING RADIUS OP GYRATION IN INCHES. 
 
 2 
 
 .78 
 
 .74 
 
 .71 
 
 .68 
 
 .65 
 
 .63 
 
 .61 
 
 .59 
 
 .58 
 
 .58 
 
 3 
 
 1.18 
 
 1.14 
 
 1.11 
 
 1.08 
 
 1.04 
 
 1.01 
 
 .98 
 
 .96 
 
 .93 
 
 .91 
 
 4 
 
 1.59 
 
 1.55 
 
 1.51 
 
 1.47 
 
 1.44 
 
 1 41 
 
 1.38 
 
 1.35 
 
 1.32 
 
 1.29 
 
 5 
 
 2.00 
 
 1.96 
 
 1.92 
 
 1.89 
 
 1.85 
 
 1 81 
 
 1.78 
 
 1.75 
 
 1.71 
 
 1.68 
 
 6 
 
 2.41 
 
 2.37 
 
 2.33 
 
 2.29 
 
 2.25 
 
 2.21 
 
 2.18 
 
 2.15 
 
 2.11 
 
 2.08 
 
 7 
 
 2 82 
 
 2.78 
 
 2.74 
 
 2.70 
 
 2.66 
 
 2.62 
 
 2.58 
 
 2.55 
 
 2.51 
 
 2.48 
 
 8 
 
 3. -23 
 
 3.19 
 
 3.15 
 
 3.11 
 
 3.07 
 
 3.03 
 
 2.9'.t 
 
 2.96 
 
 2.92 
 
 2.89 
 
 9 
 
 3.63 
 
 3 59 
 
 3.55 
 
 3.51 
 
 3.48 
 
 3.44 
 
 3 40 
 
 3.36 
 
 3.32 
 
 3 29 
 
 10 
 
 4.04 
 
 4.00 
 
 3.96 
 
 3.92 
 
 3.88 
 
 3.84 
 
 3.80 
 
 3.77 
 
 3.73 
 
 3.70 
 
 11 
 
 4.45 
 
 4.41 
 
 4.37 
 
 4.33 
 
 4.29 
 
 4.25 
 
 4.21 
 
 4.17 
 
 4.13 
 
 4.10 
 
 12 
 
 4.86 
 
 4.82 
 
 4.78 
 
 4.74 
 
 4.70 
 
 4.66 
 
 4.62 
 
 4.58 
 
 4.544.51 
 
156 
 
 TABLES OF STRUTS. 
 
 No. 17. 
 ROUND COLUMNS. 
 
 GREATEST SAFE LOADS IN LBS. PER SQ. IN. OF SECTION. 
 
 By this table for the same ratios of - the safe loads are increased 10 per 
 cent, over the results obtained for previous tables, as given in table No. 2. 
 
 SIZE 
 
 OUTKU 
 
 DIAME- 
 TER. 
 
 CONDITION 
 
 OF 
 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 13350 
 13350 
 12670 
 11660 
 
 12640 
 12640 
 12000 
 10890 
 
 11570 
 11570 
 10740 
 9330 
 
 9940 
 9940 
 8970 
 7330 
 
 8840 
 8820 
 7660 
 5790 
 
 7860 
 7050 
 6310 
 4490 
 
 6190 
 5640 
 4290 
 
 2580 
 
 3230 
 2720 
 1570 
 890 
 
 14 
 
 16 
 
 18 
 
 12" 
 
 Diameter. 
 1" thick.. 
 
 R=3-4 
 
 10" 
 
 Diameter, 
 i" thick.. 
 
 R = 3-37 
 
 8" 
 
 Diameter. 
 
 i" thick.. 
 
 R = 2-8 
 
 6" 
 
 Diameter. 
 f ' thick.. 
 
 R=2-00 
 
 5" 
 
 Diameter, 
 f" thick . 
 R = i-4 
 
 4" 
 
 Diameter. 
 J" thick.. 
 
 R^l 33 
 
 3" 
 
 Diameter. 
 W thick. 
 R = i-oo 
 
 2" 
 Diameter 
 I" thick.. 
 ll=- 
 
 Fixed Ends 
 
 
 
 15220 
 15220 
 14680 
 13940 
 
 14630 
 14630 
 140:30 
 13200 
 
 13490 
 13490 
 12810 
 11820 
 
 12140 
 12140 
 113(50 
 10080 
 
 11090 
 11090 
 10250 
 8720 
 
 9940 
 9940 
 8970 
 7330 
 
 8440 
 8400 
 7110 
 5310 
 
 6140 
 
 5f>80 
 4220 
 2540 
 
 14.330 
 14330 
 13700 
 12840 
 
 13490 
 13490 
 12810 
 11820 
 
 12440 
 12440 
 11680 
 10480 
 
 11000 
 11000 
 10150 
 8600 
 
 9850 
 9850 
 8880 
 7230 
 
 8740 
 8710 
 7520 
 5750 
 
 7330 
 
 6880 
 5560 
 3780 
 
 4510 
 37^0 
 2420 
 1390 
 
 12640 
 12640 
 12000 
 10890 
 
 11940 
 11940 
 11140 
 9820 
 
 10730 
 10730 
 9850 
 8-280 
 
 9050 
 9040 
 7960 
 6220 
 
 8150 
 8060 
 6710 
 4880 
 
 7040 
 6560 
 5240 
 3460 
 
 5110 
 4400 
 2990 
 1720 
 
 2290 
 2020 
 1100 
 630 
 
 12040 
 12040 
 11250 
 9950 
 
 11280 
 11280 
 10450 
 8960 
 
 9940 
 9940 
 8970 
 7330 
 
 8440 
 8400 
 7110 
 5310 
 
 7460 
 7260 
 5920 
 4130 
 
 6190 
 5640 
 4290 
 2580 
 
 41:30 
 3440 
 2160 
 
 1230 
 
 17IX) 
 1440 
 790 
 440 
 
 11470 
 11470 
 10840 
 9200 
 
 10640 
 10640 
 9750 
 8170 
 
 9200 
 9200 
 8170 
 6460 
 
 7860 
 7650 
 6310 
 4490 
 
 6740 
 6270 
 4920 
 3150 
 
 5400 
 4680 
 3260 
 
 1880 
 
 3300 
 2780 
 1610 
 910 
 
 1340 
 990 
 600 
 330 
 
 Flat Ends 
 Hinged Ends.. . 
 
 
 
 
 
 
 
 Round Ends 
 
 
 
 
 Fixed Ends 
 Flat Ends 
 
 
 
 .... 
 
 15660 
 15660 
 15160 
 14470 
 
 14770 
 14770 
 14190 
 13380 
 
 13490 
 13490 
 12810 
 11820 
 
 12540 
 12540 
 11790 
 10620 
 
 11570 
 11570 
 10740 
 9330 
 
 9940 
 9940 
 8970 
 7330 
 
 7820 
 7590 
 6240 
 4430 
 
 Hinged Ends... 
 Round Ends. . . 
 
 
 Fixed Ends 
 
 
 
 Flat Ends 
 
 
 
 Hinged Ends.. 
 
 
 
 Round Ends. 
 
 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends . 
 
 
 15220 
 
 15220 
 14680 
 13940 
 
 14470 
 14470 
 13870 
 13020 
 
 13490 
 13490 
 12810 
 11820 
 
 12140 
 12140 
 11360 
 10080 
 
 9850 
 98.50 
 8880 
 7230 
 
 Round Ends. 
 
 
 Fixed Ends 
 Fhit Ends 
 
 
 Kin ired Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends 
 
 
 
 Round Ends 
 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends . , 
 Round Ends. . . 
 
 Fixed Ends. .. 
 Flat Ends.. .. 
 Hinged Ends* . . 
 Round Ends. . . 
 
 15220 
 
 15220 
 14680 
 13940 
 
 13490 
 13490 
 12810 
 11820 
 
TABLES OF STRUTS. 157 
 
 No. 17. 
 ROUND COLUMNS. 
 
 GREATEST SAFE LOADS IN LBS. PER SQ. IN. OF SECTION. 
 
 The calculations are based on the thicknesses and radii of gyration marked 
 under the diameters on marginal columns. See description. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 OP 
 
 ENDS. 
 
 SIZE 
 OUTER 
 DIAME- 
 TER. 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 10910 
 
 10370 
 
 9850 
 
 9350 
 
 8990 
 
 8640 
 
 8340 
 
 8050 
 
 7770 
 
 Fixed Ends 
 
 12" 
 
 10910103701 9850 9350 
 
 8980 
 
 8610 
 
 8290 
 
 79HO 
 
 7520 
 
 Flat Ends 
 
 Diameter. 
 
 10050 
 8490 
 
 9-160 8880 8330 
 7850) 7230 ! 6640 
 
 7880 
 6030 
 
 7390 
 5610 
 
 6970 
 5150 
 
 6570 
 4750 
 
 6180 
 4370 
 
 Hinged t nds.. . 
 Round Ends 
 
 |" thick. 
 
 R 3-94 
 
 10020 
 
 9430 
 
 8990 
 
 8620 
 
 8:50 
 
 7910 
 
 76CO 
 
 7280 
 
 6940 
 
 Fixed Ends... 
 
 10" 
 
 10020 
 
 9430 
 
 8980 
 
 8610 
 
 8190 
 
 7720 
 
 7260 6830 
 
 6460 Flat Ends Diameter. 
 
 9070 
 
 8430 
 
 78SO 
 
 7390 
 
 6840 
 
 6380 
 
 6980 
 
 5510 
 
 5130!Hinged Ends. . . *" thick. 
 
 7430 
 
 6740 
 
 6030 
 
 5610 
 
 5010 
 
 4560 
 
 4130 
 
 3730 
 
 3350 
 
 Round Ends 
 
 R = 3 ' 37 
 
 
 
 
 
 
 
 
 
 
 
 811 
 
 8740 
 
 8290 
 
 7860 
 
 7460 
 
 7040 
 
 6610 
 
 6190 
 
 5790 
 
 5400 
 
 Fixed Ends... 
 
 
 8710 
 
 8250 
 
 r .650 
 
 7070 
 
 6560 
 
 6110 
 
 5640 
 
 5140 
 
 4680 Flat Ends Diameter. 
 
 7520 
 5750 
 
 6900 
 5090 
 
 6310 
 4490 
 
 5920 
 3960 
 
 5240 
 3460 
 
 4780 
 3000 
 
 4290 
 2580 
 
 3750 
 2210 
 
 3260 Hinged Ends... 
 1880 1 Round Ends 
 
 i" thick. 
 
 XV ~ ^ ' ** 
 
 7330 
 
 6740 
 
 6190 
 
 5660 
 
 5110 
 
 4580 
 
 4130 
 
 3700 
 
 3300'Fixed Ends... 
 
 6" 
 
 6880 
 
 6:70 5640 
 
 4990 
 
 4400 
 
 3850 
 
 3440 
 
 3C80i 2780 Flat Ends Difimeter. 
 
 5560 
 3780 
 
 4920 
 3150 
 
 4290 
 2580 
 
 3580 
 2090 
 
 2990 
 1720 
 
 2470 
 1440 
 
 2160 
 1230 
 
 1880 
 1C40 
 
 161()iHiiigedEids... 
 910.Round Ends 
 
 | thick. 
 R = a-uo 
 
 6100 
 
 5440 
 
 4760 
 
 4210 
 
 3670 
 
 3160 
 
 2^90 
 
 2420 
 
 2110 ! Fixed Ends 
 
 5" 
 
 55301 4730 1 4020 
 
 3500 
 
 3050 
 
 2680 
 
 2380 
 
 2110 
 
 1870!Flat Ends Diameter. 
 
 4160 
 2490 
 
 33101 2640 
 1900 1520 
 
 2220 
 1260 
 
 1850 
 1030 
 
 1540 
 860 
 
 1330 
 750 
 
 1150 
 660 
 
 1000 
 
 580 
 
 H nged Ends... 
 Round Ends 
 
 StfRft 
 
 4580 
 
 3880 3260 
 
 2770 
 
 2320 
 
 2000 
 
 1780 
 
 1560 
 
 1360 
 
 Fixed Ends... . 
 
 4" 
 
 3850 
 
 3210 
 
 2750 
 
 2370 
 
 2040 
 
 1740 
 
 1470 
 
 1220 
 
 1010 
 
 Flat Ends 
 
 Diameter. 
 
 2470 
 1440 
 
 2000 
 1110 
 
 1590 
 900 
 
 13:0 
 740 
 
 1110 
 630 
 
 940 
 530 
 
 800 
 450 
 
 690 
 380 
 
 610 
 330 
 
 Hinged Ends... 
 Round Ends. . . . 
 
 i" thick. 
 
 R= i'33 
 
 2650 
 
 2100 
 
 1790 
 
 1500 
 
 1240 
 
 1070 
 
 910 
 
 770 
 
 
 Fixed Ends.... 
 
 3" 
 
 2270 
 
 1850 
 
 1480 
 
 1150 
 
 910 
 
 710 
 
 530 
 
 440 
 
 
 Flat Ends 
 
 Diameter. 
 
 1250 
 
 1000 810 
 
 670 
 
 560 
 
 460 3.50 
 
 2801 .., 
 
 Hinged Ei els.. . 
 
 -fa" thick. 
 
 710 
 
 580 
 
 450 
 
 370 
 
 290 
 
 2501 200 
 
 170 
 
 
 Round Ends 
 
 R=i-oo 
 
 1040 
 
 810 
 
 
 
 
 
 
 
 
 Fixed Ends.. .. 
 
 9" 
 
 *"* 
 
 680 
 
 470 
 
 
 
 
 
 
 
 Flnt Ends 
 
 
 440 300 
 240 180 
 
 1 
 
 
 
 
 
 
 
 Hinged Ends... 
 Round Ends.. . . 
 
 Dintn^tcr. 
 t" thick. 
 
 T? _ 66 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 J\ 
 
158 
 
 TABLES OF STEUTS. 
 
 No. 18. 
 SQUARE COLUMNS. 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE INCH OF SECTION. 
 
 By this table for the same ratios of , the safe loads are increased 5 per 
 cent, over the results obtained in table No. 2. 
 
 SIZE 
 
 OF 
 
 COLUMN. 
 
 CONDITION 
 
 OP 
 
 ENDS. 
 
 LENGTH IN FEET. 
 
 2 
 
 4 
 
 10330 
 10330 
 9500 
 8010 
 
 12160 
 12160 
 11460 
 10400 
 
 13540 
 13540 
 12940 
 12100 
 
 14390 
 14390 
 13860 
 13120 
 
 14950 
 14950 
 14480 
 13820 
 
 6 
 
 8 
 
 6760 
 6320 
 5060 
 3360 
 
 8690 
 8680 
 7660 
 6020 
 
 10330 
 10330 
 9500 
 8010 
 
 11310 
 11310 
 10540 
 9260 
 
 12160 
 12160 
 1 1460 
 10390 
 
 13540 
 13540 
 12940 
 12100 
 
 14380 
 14380 
 13S60 
 13120 
 
 14950 
 14950 
 14480 
 13820 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 2" 
 
 i" thick.. 
 R = 
 
 3" 
 
 ^thick 
 
 4" 
 
 }" thick.. 
 
 R= 1-53 
 
 5" 
 
 t" thick.. 
 
 R = ! 
 
 6" 
 
 t" thick.. 
 
 .R=2-30 
 
 8" 
 
 J" thick.. 
 
 R = 3-07 
 
 10" 
 
 i" thick.. 
 
 R=3-7 
 
 12" 
 
 4" thick.. 
 
 R = 4-56 
 
 Fixed Ends.... 
 Flat Ends 
 
 13540 
 13540 
 12910 
 12100 
 
 14950 
 14950 
 14480 
 13810 
 
 8160 
 8120 
 6920 
 5210 
 
 10330 
 10330 
 9500 
 8010 
 
 11690 
 11690 
 10940 
 9750 
 
 12610 
 12610 
 11950 
 10960 
 
 13540 
 13540 
 12940 
 12100 
 
 14670 
 14670 
 14170 
 13470 
 
 5410 
 4770 
 3420 
 2000 
 
 7690 
 7570 
 6280 
 4540 
 
 9010 
 9010 
 8050 
 6440 
 
 10250 
 10250 
 9410 
 7910 
 
 11220 
 1122G 
 10450 
 9150 
 
 12480 
 12480 
 11800 
 10800 
 
 13540 
 13>40 
 12940 
 12100 
 
 14250 
 14250 
 13700 
 12950 
 
 4130 
 
 i 3440 
 2180 
 1250 
 
 6760 
 6323 
 5060 
 3360 
 
 8150 
 8HO 
 6920 
 5210 
 
 9170 
 9170 
 8220 
 66:30 
 
 10330 
 10330 
 9500 
 8010 
 
 11690 
 11690 
 10940 
 9750 
 
 12750 
 12750 
 12090 
 11130 
 
 13420 
 13420 
 12800 
 11930 
 
 3090 
 2600 
 1500 
 850 
 
 5830 
 5280 
 3980 
 2380 
 
 7420 
 7180 
 5900 
 4180 
 
 8400 
 8370 
 7260 
 5460 
 
 9410 
 9410 
 84*0 
 6910 
 
 10950 
 10950 
 10160 
 8790 
 
 12060 
 2060 
 1360 
 10270 
 
 2750 
 2750 
 12090 
 11130 
 
 2310 
 2020 
 1100 
 630 
 
 4920 
 
 4240 
 2900 
 1680 
 
 6720 
 6220 
 5010 
 3310 
 
 7780 
 7700 
 6400 
 4660 
 
 8690 
 8680 
 7660 
 6020 
 
 10250 
 10250 
 9410 
 8010 
 
 11400 
 11400 
 10(540 
 9380 
 
 12140 
 12140 
 11460 
 10400 
 
 1790 
 1510 
 820 
 450 
 
 4080 
 3410 
 2160 
 1240 
 
 6040 
 5540 
 4260 
 2590 
 
 7260 
 6930 
 5660 
 3950 
 
 8160 
 8120 
 6920 
 5210 
 
 9650 
 9650 
 8750 
 7190 
 
 10860 
 10860 
 10070 
 8670 
 
 11690 
 116M) 
 10940 
 9750 
 
 Hinged Ends... 
 Round Ends 
 
 Fixed Ends 
 Flat Ends 
 Hinged Ends... 
 Round End* 
 
 Fixed Ends 
 
 Flat Ends . 
 
 
 Hinged Ends.. . 
 Round End* 
 
 
 Fixed Ends 
 
 
 Flat Ends 
 Hinged Ends. .. 
 Round Ends 
 
 
 
 Fixed Ends 
 
 
 Flat Ends 
 Hinged Knds 
 
 
 
 Round Ends 
 
 
 Fixed Ends 
 
 
 Flat Ends. .. 
 
 
 
 rlinged Ends 
 
 
 
 Round Ends. . 
 
 
 Fixed Ends ... 
 
 
 
 Flat Ends 
 
 
 
 
 Hinged Ends... 
 
 
 
 
 Round Ends 
 
 
 
 
 Fixed Ends.... 
 
 
 
 
 Flat Ends 
 
 
 
 
 Hinge< 1 Ends. .. 
 
 
 
 
 Round Ends. . . 
 
 
 
 
 
 
 
 
TABLES OF STR 
 
 No. 18. 
 SQUARE COLUM 
 
 GREATEST SAFE LOAD IN LBS. PER SQUARE 
 
 The calculations are based on the thicknesses and radii of gyration, 
 marked under the diameters in marginal columns-. See preceding descrip- 
 tion. 
 
 LENGTH IN FEET. 
 
 CONDITION 
 
 SIZE 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 j 32 
 
 34 
 
 36 
 
 OP 
 
 ENDS. 
 
 OP 
 
 COLUMN. 
 
 1440 
 
 1120 
 
 930 
 
 760 
 
 
 
 
 
 
 Fixed Ends.... 
 
 0" 
 
 1100 810 
 
 580 
 
 430 
 
 
 
 
 
 
 Flat Ends 
 
 J 
 
 640 490 
 360 260 
 
 380 
 210 
 
 270 
 170 
 
 
 
 
 
 
 Hinged Ends... 
 Round Ends 
 
 I" thick. 
 K- " 
 
 
 
 
 
 8380 2770 
 
 2290 
 
 1910 
 
 1660 
 
 1430 
 
 1210 
 
 1060 
 
 910 
 
 Fixed Ends... 
 
 0" 
 
 2820 2360 
 
 2010 
 
 1670 
 
 1370 
 
 1090 
 
 880 
 
 710 
 
 560 
 
 Flat Ends 
 
 o 
 
 16901 1320 
 
 1090 
 
 900 
 
 750 
 
 630 
 
 550 
 
 450 
 
 370 
 
 Ringed Ends. .. 
 
 tV' thick 
 
 950 760 
 
 630 
 
 510 
 
 420 
 
 360 
 
 290 
 
 240 
 
 210 
 
 Round Ends 
 
 R= > 
 
 5370 4670 
 
 4080 
 
 3540 
 
 3020 
 
 2650 
 
 2250 
 
 1960 
 
 1770 
 
 FMxed Ends. ... 
 
 A" 
 
 4710 3980 
 
 3110 
 
 2940 
 
 2560 
 
 2270 
 
 1980 
 
 1730 
 
 1500 
 
 Flat Ends 
 
 TE 
 
 a37o 
 
 1950 
 
 8850 
 
 1530 
 
 2160 
 1240 
 
 1800 
 1000 
 
 1470 
 830 
 
 1260 
 710 
 
 1080 
 620 
 
 930 
 540 
 
 810 
 450 
 
 linged Ends. .. 
 iound Ends 
 
 i" thick. 
 R- * 
 
 6670 
 
 6130 
 
 5580 
 
 5020 
 
 4500 
 
 4020 
 
 3570 
 
 3150 
 
 2790 
 
 Fixed Ends.... 
 
 K'<i 
 
 6230 
 
 5650 
 
 4970 
 
 4340 
 
 3800 
 
 8350! 2970 
 
 2660 
 
 2370 
 
 Flat Ends 
 
 O 
 
 49(50 
 3460 
 
 4370 
 2680 
 
 3630 
 2140 
 
 2990 
 1720 
 
 2480 
 1440 
 
 2120 1820 
 1210 1010 
 
 1540 
 870 
 
 1330 
 760 
 
 linged Ends.. . 
 Round Ends. . . . 
 
 f " thick. 
 R= i-fc 
 
 7690 
 
 7210 
 
 6760 
 
 6310 
 
 5830 
 
 5410! 4920 
 
 4500 
 
 4080 
 
 Fixed Ends.... 
 
 fi" 
 
 7570 
 
 6880 1 6320 
 
 5840 5280 
 
 4770 
 
 4240 
 
 3800 
 
 3410 
 
 Flat Ends 
 
 u 
 
 6280 
 4540 
 
 5610 
 3900 
 
 5060 
 3360 
 
 4570 
 2870 
 
 3980 
 2380 
 
 3420 
 2000 
 
 2900 
 2390 
 
 2480 
 1440 
 
 2160 
 1240 
 
 Hinged Ends... 
 Round Ends 
 
 I" thick. 
 R = a-30 
 
 9010 
 
 8550 
 
 8160 
 
 7820 
 
 7470 
 
 7130 
 
 6760 
 
 6390 
 
 6040 
 
 Fixed Ends... 
 
 Q" 
 
 9010 
 
 8530 
 
 8120 
 
 7760 
 
 7250 
 
 6750 
 
 6320 
 
 5930 
 
 5540 
 
 Flat End.* 
 
 O 
 
 8050 
 &430 
 
 7450 
 5690 
 
 69:20 
 5210 
 
 6470 
 4730 
 
 5960 
 4230 
 
 5480 
 3780 
 
 5060 
 3360 
 
 4660 
 2960 
 
 426' > 
 2590 
 
 Hinired Ends... 
 Round Ends. . . . 
 
 *" thick. 
 
 R=3'OT 
 
 10330 
 
 9820 
 
 9320 
 
 8790 
 
 8490 
 
 8200 
 
 7920 
 
 7640 
 
 7340 
 
 Fixed Ends... 
 
 10" 
 
 10330 
 
 98-20 
 
 9320 
 
 87W 
 
 8470 
 
 8170 
 
 7870 
 
 7500 
 
 7060 
 
 Flat Ends 
 
 J.U 
 
 9500 
 
 8010 
 
 8!40 
 7390 
 
 8400 
 6810 
 
 7800 
 6170 
 
 7390 
 5620 
 
 6980 
 5280 
 
 6590 
 4860 
 
 6220 
 4480 
 
 5780 
 4060 
 
 Hinged Ends. .. 
 Round Ends.... 
 
 i" thick. 
 
 R=8-8T 
 
 11130 
 
 10680 
 
 10250 
 
 9730 
 
 9320 
 
 8920 
 
 8640 
 
 8350 
 
 8110 
 
 Fixed Ends... 
 
 1 9" 
 
 11130!10680 10250 
 
 9730 9320 
 
 8920 8630 
 
 8320 
 
 8060 Flat Ends 
 
 1 ft 
 
 10350 
 9030 
 
 9880 
 8440 
 
 9410 
 7910 
 
 8840 
 7300 
 
 8400 
 6810 
 
 7960 
 6340 
 
 7600 
 5940 
 
 7180 
 5490 
 
 6860 
 5130 
 
 Hinged Ends... 
 Round Ends.... 
 
 f" thick. 
 
 R=4-65 
 
160 WROUGHT IRON AND STEEL. 
 
 RIVETS AND PINS. 
 
 Rivets must be proportioned with sufficient bearing surface to 
 resist crushing, and sufficient sectional area to resist shearing. 
 Pins must be proportioned likewise, and also to safely resist the 
 bending action which usually exists, owing to the centres of 
 pressure being some distance from the centres of supports. 
 
 The effective bearing area of a rivet or pin is equal to its di- 
 ameter multiplied by the thickness of the surface it bears on. 
 
 The shearing area is the area of the cross section of the pin or 
 rivet for single shear, or double that section for double shear. 
 For pins, the pressure on the pins multiplied by the leverage 
 with which it acts on the pin supports is the bending moment. 
 (See bending moments, page 78.) 
 
 The ultimate crushing strength of wrought iron is taken as 
 equal to its tensile strength, viz., 50,000 Ibs. per square inch, 
 the shearing strength at -ft,- of same, viz., 40,000 Ibs. per 
 square inch. The ultimate modulus of rupture is taken at 
 50,000, which is a fair estimate for cylindrical sections, as the 
 average of many experiments we have made on that shape gives 
 nearly that amount. The annexed table gives the ultimate 
 resistance for single shear, or the area of the pin multiplied by 
 40,000, and the ultimate resistance to crushing, for each inch in 
 thickness of bearing surface, or the diameter of the pin multi- 
 plied by 50,000. 
 
 The ultimate bending moments in inch Ibs. correspond to the 
 given diameter of pins, and are derived from the formula 
 
 50,0007 
 
 M. = ~ . 
 
 radius 
 
 which can be reduced to this form, 
 
 M = 6250 x area x diameter, all in inches. 
 
 To obtain the working resistances, these ultimate values must 
 be divided by the factor of safety desirable to use. 
 
 The following proportions of the ultimate strength are com- 
 monly used for the purposes named. 
 
RIVETS AND PINS. 161 
 
 For K. R. bridges, 
 
 For light highway bridges, 
 
 For roof trusses, etc., 
 
 of ultimate strength, 
 of " " 
 
 of " 
 
 Example. A pin has its supports located three inches apart, 
 and bears a load of 100,000 Ibs. in the middle. What should 
 the diameter of the pin be for a safety factor of five ? 
 
 Bending moment = 100>00 ^ x 3 " = 75,000 inch Ibs. 
 
 The nearest diameter corresponding to this and taking 3 of 
 the tabular moments, is 4^ inches. 
 
 The bearing value of this pin is ( of table) 42,500 Ibs. per 
 inch of length, consequently the thickness of the metal which 
 forms the pin bearings should be -^W 1 , or not less than 2.3 
 inches. For shear the pin has a large excess of strength, which 
 will usually be found the case if properly proportioned other- 
 wise. 
 
 11 
 
162 
 
 WROUGHT IRON AND STEEL. 
 
 ULTIMATE STEENGTH OF RIVETS AND PINS OF 
 WROUGHT IRON. 
 
 For the working strength divide the tabular figures by the desired factor of 
 safety. 
 
 DIAMETER 
 IN INCHES 
 
 OF RIVET 
 OR PIN. 
 
 AREA IN 
 SQUARE 
 INCHES. 
 
 ULTIMATE 
 STRENGTH FOR 
 SINGLE SHEAR 
 
 IN LBS. 
 
 ULTIMATE 
 CRUSHING 
 STRENGTH PER 
 
 INCH THICKNESS 
 
 OF BEARING 
 SURFACE. 
 
 ULTIMATE 
 BENDING MO- 
 MENT IN 
 INCH LBS. 
 
 X 
 
 .196 
 
 7840 
 
 25000 
 
 614 
 
 
 .248 
 
 9920 
 
 28125 
 
 873 
 
 y 
 
 .307 
 
 12280 
 
 31250 
 
 1199 
 
 ii 
 
 .371 
 
 14840 
 
 34375 
 
 1595 
 
 % 
 
 .442 
 
 17680 
 
 37500 
 
 2073 
 
 \\ 
 
 .518 
 
 20720 
 
 40625 
 
 2632 
 
 % 
 
 .601 
 
 24040 
 
 43750 
 
 3287 
 
 1 inch. 
 
 .785 
 
 31400 
 
 50000 
 
 4906 
 
 % 
 
 .994 
 
 39760 
 
 56250 
 
 6993 
 
 * 
 
 1.227 
 
 49080 
 
 62500 
 
 9586 
 
 % 
 
 1.485 
 
 59400 
 
 68750 
 
 12762 
 
 % 
 
 1.767 
 
 70680 
 
 75000 
 
 1H566 
 
 % 
 
 2.074 
 
 82960 
 
 81250 
 
 21065 
 
 % 
 
 2.405 
 
 96200 
 
 87500 
 
 26305 
 
 % 
 
 2.761 
 
 110440 
 
 93750 
 
 32357 
 
 2 inches. 
 
 3.141 
 
 125660 
 
 100000 
 
 39263 
 
 % 
 
 3.547 
 
 141880 
 
 106250 
 
 47109 
 
 X 
 
 3.976 
 
 159040 
 
 112500 
 
 55913 
 
 
 4.430 
 
 177200 
 
 118750 
 
 65757 
 
 % 
 
 4.908 
 
 196320 
 
 125000 
 
 76688 
 
 % 
 
 5.412 
 
 216480 
 
 131250 
 
 88792 
 
 K 
 
 5.940 
 
 237600 
 
 137500 
 
 102094 
 
 
 6.492 
 
 259680 
 
 143750 
 
 116825 
 
 3 inches. 
 
 7.068 
 
 282720 
 
 150000 
 
 132426 
 
 ^ 
 
 7.670 
 
 806800 
 
 156250 
 
 149694 
 
 % 
 
 8.296 
 
 331840 
 
 162500 
 
 168514 
 
 % 
 
 8.946 
 
 357840 
 
 168750 
 
 188705 
 
 
 9.621 
 
 384840 
 
 175000 
 
 210459 
 
 % 
 
 10.321 
 
 412840 
 
 181250 
 
 233835 
 
 & 
 
 11.045 
 
 441800 
 
 187500 
 
 258909 
 
 % 
 
 11.793 
 
 471720 
 
 193750 
 
 285613 
 
 4 inches. 
 
 12.566 
 
 502640 
 
 200000 
 
 314150 
 
 * 
 
 13.364 
 
 534560 
 
 206250 
 
 344540 
 
 
 14.186 
 
 567440 
 
 2125CO 
 
 376816 
 
 % 
 
 15.033 
 
 601320 
 
 218750 
 
 411057 
 
 % 
 
 15.904 
 
 636160 
 
 225000 
 
 447300 
 
 % 
 
 16.800 
 
 672000 
 
 231250 
 
 485623 
 
 * 
 
 17.721 
 
 708840 
 
 237500 
 
 526092 
 
 
 18.665 
 
 746600 
 
 243750 
 
 568700 
 
 5 inches. 
 
 19.635 
 
 785400 
 
 250000 
 
 613600 
 
 
 20.629 
 
 825160 
 
 256-250 
 
 660773 
 
 IX 
 
 21.648 
 
 865920 
 
 26-2500 
 
 710326 
 
 % 
 
 22.691 
 
 907640 
 
 268750 
 
 762266 
 
 IX 
 
 23.758 
 
 950320 
 
 275000 
 
 816667 
 
 / 
 
 24.850 
 
 994000 
 
 281250 
 
 873627 
 
 y 
 
 25.967 
 
 1038680 
 
 287500 
 
 933189 
 
 6 inches. 
 
 27.109 
 
 28.274 
 
 1084360 
 1130960 
 
 21)3750 
 300000 
 
 995410 
 1060277 
 
STRESSES IN TEAMED STEUCTURES. 163 
 
 STEESSES IN SOME SIMPLE FORMS OF FRAMED 
 STRUCTURES. 
 
 Compression indicated by the sign and by solid lines. 
 Tension by the sign + and by dotted lines. 
 
 When the prefix "stress" is used, the load borne by the 
 member is indicated; otherwise the length of the member is 
 meant. 
 
 CRANES. 
 
 Supported at the points A and B, maximum longitudinal 
 stresses, due to weight W, suspended at the end. These stresses 
 are modified by the position of the hoisting chain. 
 
 FIG.1 
 
 E/ 
 
 D is the point where a line drawn from C at right angles to 
 A B will intersect the latter. 
 
 Stress AC=+ -? x W Stress B G = x W 
 
 " AB= + x TF in Fig. 2, or = - x TFinFig.3. 
 
 .0. Jj *a. _D 
 
 When point A is supported by inclined back stays as shown 
 in Fig. 1, and when the back stay is in the plane of A B and W 
 
 Stress A E = + ~ x W x 4- 
 
 yl JD _fy JrJ 
 
 and a resulting compression ensues on 
 
 A B = ~ - x W x 
 
164 
 
 WROUGHT IBON AND STEEL. 
 
 CRANES. 
 
 CD 
 
 FIG.4 
 
 Stress CD=- 
 
 'AD 
 
 W 
 
 v " E D = - stress D 0. 
 
 Let w = the horizontal reaction at B 
 CD 
 
 w = 
 
 AB 
 
 xW 
 
 B E 
 Stress B E = + -=-= x 
 
 J2J JJ 
 
 A E = + --, x (stress CD - w) 
 
 E and H are points where 
 lines drawn from D intersect 
 at right angles A C and A B. 
 X, Y and Z are the angles 
 formed by extending the braces 
 CD and B D as indicated by 
 dotted lines, w = the hori- 
 zontal reaction at B 
 
 AB 
 
 Stress A C= + ^ x W. Stress C D = - C D 
 
 A D= 
 
 or = 
 
 + B H x w 
 stress C D x 
 - stress B D x 
 
 BD 
 
 Sine T 
 Sine JT 
 
 Sine F 
 SineZ 
 
 BD 
 
STRESSES IN FRAMED STRUCTURES. 165 
 
 TRUSSED GIRDERS. 
 Weight in Middle. 
 FIG. 6 Stress A C or 
 
 fty B D ^ .AC W 
 
 W 
 
 " DC=-W 
 
 Weight out of Centre. 
 
 FIG. 7 
 
 w, 
 
 AB x 
 
 = - w 
 
 FIG. 8 
 
 W. W. 
 
 o Stress A HOT DU = + 
 
 xW 
 
 
 Stress 
 
 B H or C E-- W 
 
166 
 
 WKOUGHT IRON AND STEEL. 
 
 TRUSSED GIRDERS. 
 Unequal Loads W and w. 
 
 FIG. 9 
 
 Stress as below on counter 
 diagonals B E orHC according 
 to position of greatest load. 
 
 CH fW-w\ 
 
 Stress <7tf= 
 
 FIG. 10 
 
 
 
 Fink Truss. 
 
 Stress B For D H W 
 
 E 
 
 O = -2 W 
 
 ID stress 1 
 
 '= -14 Wx 
 
 Stress ^1 jPor HE= 
 
 AO 
 
STRESSES IN FRAMED STRUCTURES. 167 
 
 ROOFS. 
 w load concentrated on each triangular apex. 
 
 Strut Stresses. 
 Stress D F= - w 
 
 F B G 
 
 Stresses on Ties. 
 
 Rafter Stresses. 
 
 =: + l|w x Stress CE=- 2 w 
 
 C JT 
 
168 WROUGHT IRON AND STEEL. 
 
 ROOFS. 
 
 w load concentrated on each triangular apex . 
 
 Strut Stresses. 
 
 ^ Fla ' 2 Bto-HInXL*-** 
 
 (w) 
 
 ^-SS i \ ! i ~ \ / V \~T> -r\ n 
 
 Stresses. 
 
 ft K- C B CD\ 
 
 - - x - M 'x JTB; 
 
 -_ Iw CB CD 
 
 ---*- W * 
 
 Stresses on Ties. 
 Stress 6^ /or (7 i = + -5- x 77-^ x 7^-^ 
 
 DB C B 
 1BI=+ w x 
 
 CB 
 CI = X -~ X 
 
 ^ L = the sum of the stresses on F E and ^ /. 
 L B = the sum of the stresses on E L and G L. 
 
STRESSES IN FRAMED STRUCTURES. 169 
 
 ROOFS. 
 
 w = load concentrated on each triangular apex. 
 
 The rafters and horizontal tie being each uniformly subdi- 
 vided. 
 
 Strut Stresses. 
 
 -.f x*f 
 
 Vertical Ties. 
 Stress ^ if = + Stress i> / = + i/;. Stress G B = 
 
 Rafter Stresses. 
 
 n * 
 
 Stress C D = -2 wx^ 
 
 L -D 
 ft A 
 
 " D E =. 2i w 
 
 Stress at B = + 2 w x 
 
 Horizontal Tie. 
 BA 
 
 B G 
 
 B 1= + stress at B + I stress D B x 
 
 + (> 
 
170 WROUGHT IRON AND STEEL. 
 
 WROUGHT IRON SHAFTING. 
 
 (For steel shafting see page 29.) 
 
 The ultimate resistance of wrought iron to shearing averages 
 about -ft of its ultimate tensile strength, i.e., about 40,000 
 Ibs. per sq. inch of section. The torsional resistance of any 
 wrought-iron shaft can be determined when the shearing resist- 
 ance is known ; thus, 
 
 T= .196 d*s for round shafts, (a) 
 
 T = . 28 d*s for square shafts. (b) 
 
 d diameter of the shaft in inches. 
 
 s = shearing strength in Ibs. per sq. inch. 
 
 T the torsional moment in inch-lbs., that is, the force in Ibs. 
 
 multiplied by the length in inches, of the lever through 
 
 which the force acts. 
 
 Taking s at 40,000 Ibs., and assuming that in machinery the 
 working value of wrought iron should be taken at from one- 
 fourth to one- fifth of its ultimate strength, these being factors of 
 safety sanctioned by good practice, we adopt the mean of the 
 two, which makes the working resistance to shearing = 9,000 
 Ibs. per sq. inch. Putting this in terms of the torsional moment 
 and of the diameter, we derive from equations a and b, 
 
 T = 1760 d 3 for round shafts, (c) 
 
 T = 2520 d 3 for square shafts, (d) 
 
 3 / T 
 
 y .p^Q 
 
 for round shafts, 
 
 d 4/ ^KOA f r square shafts. (/) 
 
 Example 1. What should be the diameter of a round wrought 
 
SHAFTING. 
 
 171 
 
 iron shaft to safely resist a force of 1,000 Ibs. acting through a 
 lever 30 inches long ? 
 
 -4T 
 
 1000 x 
 1700 
 
 = 2.6 inches diameter. 
 
 These formulae apply to shafts subject to twisting strains 
 alone. In practice, however, sucn cases seldom occur, as shafts 
 are generally subjected to combined bending and twisting strains. 
 As there are no experimental data for such a combination of 
 forces, we have to rely on analysis, which gives the following: 
 
 = M + 
 
 <ff) 
 
 M = bending moments in inch-lbs. (See page 78.) 
 
 T = twisting 
 
 T l = a new twisting moment which, substituted for T in equa- 
 tions (e) and (/), will give the desired proportions for 
 the shaft. 
 
 In revolving shafts the longitudinal stress resulting from the 
 bending action is continually changing from tension to com- 
 pression, and vice versa. 
 
 It is therefore advisable, for reasons given on page 34, to in- 
 crease the factor of safety as the bending stress increases com- 
 paratively to the torsional stress. 
 
 The following changes in factors of safety are recommended : 
 
 RATIO OP M TO T. 
 
 FACTOR OP SAFETY. 
 
 DIVISOK IN FORMULA (e). 
 
 M = .3T or less, 
 
 4 
 
 1760 
 
 M= .62 7 " 
 
 5 
 
 1570 
 
 M=T 
 
 51 
 
 1430 
 
 M = greater than T, 
 
 6 
 
 1310 
 
172 WROUGHT IRON AND STEEL. 
 
 Example 2. What should be the diameter of the journals of 
 a wrought-iron shaft of a steam engine. The piston being 12 
 inches diam., crank 12 inches long, and the leverage from centre 
 of crank to journal in the direction of the shaft being 6 inches, 
 steam pressure 80 Ibs. per sq. inch, making pressure on crank 
 = 9050 Ibs.? 
 
 T = 9050 x 12 = 108600 inch-lbs. 
 M = 9050 x 6 = 54300 " 
 
 (g) 7 71 = 54300 + 1/54300 a + 1086U0 2 = 175720 inch-lbs. 
 
 Substituting the above in equation (e), with the factor of safety 
 as explained above, 
 
 d = 4/ 175720 = 4.82 inches diameter. 
 V 1570 
 
 The following illustrates a case where the bending moment is 
 greater than the twisting moment : 
 
 Example 3. A non-continuous shaft is so located that it must 
 have its bearings 84 inches apart, and carry in the middle a 60- 
 inch pulley driven by a 12-inch belt, the effective weight at 
 centre of shaft = 600 Ibs., and the belt exercises a vertical pull 
 of 1000 Ibs. What is the proper diameter of the shaft ? 
 
 Jf= (1000 + 600)x84 = 33600 inch . lbs (g 
 T = 1000 x 30 = 30000 inch-lbs. 
 
 (g) T 1 = 33600 + t/33600 2 + 80000' = 78640 inch-lbs. 
 
 As M is greater than T, use a factor of safety of 6, which 
 becomes by equation (e), 
 
 d = 1/^2- = 4.12 inches diam. 
 
 ' IdlO 
 
 If above shaft was continuous and uniformly loaded, the 
 
SHAFTING. 173 
 
 bending moment would be less. (See Table of Bending Mo- 
 ments, page 80.) 
 
 HORSE POWER. 
 
 If it is desired to find the relations between horse power and 
 diameters of shafts, the elements of time and velocity have to be 
 considered. Taking the horse power HP at 396000 inch-lbs. 
 
 6.28 x T x V , Tr 
 per minute, we have HP = - Q(lfirtnn - , where V = revolu- 
 
 tions per minute. 
 rtA 
 
 h 1 
 
 y , 
 
 or in terms of the diameter by equation (c) we get, 
 
 The above will give the proper diameter of a shaft for trans- 
 mitting any desired HP when the shaft is subjected to twisting 
 stress alone, but, as previously stated, such a case seldom occurs, 
 we must combine the bending and twisting stresses, for which a 
 general rule will be given at the close of the subject. 
 
 DEFLECTION OF SHAFTING. 
 
 For continuous line shafting used for transmitting power in 
 shops, factories, etc., it is considered good practice to limit the 
 deflection to a maximum of y^ of an inch per foot of length. 
 The weight of bare shafting in Ibs. = 2.Qd-l= W, or when as 
 fully loaded with pulleys as is customary in practice, and allow- 
 ing 40 Ibs. per inch of width for the vertical pull of the belts, 
 experience shows the load in Ibs. to be about 13d~l = W. 
 Taking the modulus of transverse elasticity at 26,000,000 Ibs., we 
 can derive from the authoritative formulae the following : 
 
 I = \/STM 2 for bare shafts, (j) 
 
 1= ^/T75d~ 2 for shafts carrying pulleys, etc., (k) 
 
174 WROUGHT IRON AND STEEL. 
 
 which would be the maximum distance in feet between bearings 
 for continuous shafting subjected to bending stress alone. 
 
 If the length is fixed, and we desire the diameter of the shaft, 
 we have, 
 
 d 4/ - for bare shafting, (?) 
 
 * o7o 
 
 d = jy for shafting carrying pulleys, etc. (m) 
 
 To apply the above to revolving shafting subjected to both 
 twisting and bending stress, it is necessary to combine equations 
 (f) and (k) with equation ("). 
 
 But in shafting, with the same transmission of power, the 
 torsional stress is inversely proportional to the velocity of rota- 
 tion, while the bending stress will not be reduced in the same 
 ratio. It is, therefore, impossible to write a formula covering 
 the whole problem and sufficiently simple for practical applica- 
 tion, but the following rules are correct within the range of 
 velocities usual in practice. 
 
 WORKING FORMULA FOR CONTINUOUS SHAFTING. 
 
 For the diameter (d) in inches, and the maximum length (I) in 
 feet between bearings of wrought-iron shafting so proportioned 
 as to deflect not more than - r l off of an inch per foot of length, 
 allowance being made for the weakening effect of key seats, 
 
 /Kf) I/O 
 
 d = 4/ ^F- for bare shafts, () 
 
 3 />yf\ fj"p 
 
 d = y for shafts carrying pulleys, etc., (o) 
 
 I = ^720 2 for bare shafts, (p) 
 
 I = \/l4Qd' 2 for shafts carrying pulleys, etc., - (q) 
 
SHAFTING. 
 
 175 
 
 In the event of the whole power being received on a principal 
 shaft, the proper size of the shaft can be estimated direct by 
 formula (g). 
 
 Example 4. A principal shaft receiving 150 HP from the 
 engine, revolves 150 R. P. M., and is continuous over bearings 
 located 6 feet apart, the centre of main pulley being 24 inches 
 from one bearing and 48 inches from the other. The effective 
 loa 1 at the centre of the pulley resulting from weight of pulley 
 and shaft, and tension of belt, is 1500 Ibs. What should be the 
 diameter of the shaft ? 
 
 Note. Excepting special cases which rarely occur in practice, 
 it is best to treat such shafts as non-continuous. 
 
 By rule 5, page 79, we have, 
 Jf = WOOx:S4x_48 
 
 tit 
 
 and by formula (7t) we have, 
 
 150 
 then, by formula (g) we have 
 
 T>= 24000 + ^24000 2 + 63000" = 92290 inch-lbs. 
 and by formula (), 
 
 BELTING. 
 
 When designing shafting, allow for the tension of belting, 
 50 Ibs. per inch of width for single leather belt or its equivalent, 
 or 80 Ibs. per inch of width for double leather belt, or its equi- 
 valent of other material. 
 
176 
 
 WROUGHT IRON AND STEEL. 
 
 WORKING PROPORTIONS FOR CONTINUOUS 
 SHAFTING. 
 
 TRANSMITTING POWER, BUT SUBJECT TO NO BENDING ACTION 
 EXCEPT ITS OWN WEIGHT. 
 
 DIAMETER 
 or SHAFT IN 
 INCHES. 
 
 MAX. SAFE TOR- 
 SIONAL MOMENT 
 IN INCH-POUNDS. 
 
 REVOLU' 
 100 
 
 [IONS PER MINUTE. 
 
 150 | 200 
 
 MAX. DIS- 
 TANCE IN 
 FEET 
 
 BETWEEN 
 
 BEARINGS. 
 
 HP 
 
 HP 
 
 HP 
 
 H 
 
 5940 
 
 6 
 
 10 
 
 14 
 
 11.7 
 
 If 
 
 7552 
 
 9 
 
 13 
 
 17 
 
 12.4 
 
 n 
 
 9433 
 
 11 
 
 16 
 
 21 
 
 13.0 
 
 tt 
 
 11602 
 
 13 
 
 20 
 
 26 
 
 13.6 
 
 2 
 
 14080 
 
 16 
 
 24 
 
 32 
 
 14.2 
 
 2i 
 
 16892 
 
 19 
 
 29 
 
 38 
 
 14.8 
 
 at 
 
 20048 
 
 23 
 
 34 
 
 46 
 
 15.4 
 
 2| 
 
 23580 
 
 27 
 
 40 
 
 54 
 
 16.0 
 
 3i 
 
 27500 
 
 31 
 
 47 
 
 63 
 
 16.5 
 
 2* 
 
 36603 
 
 42 
 
 62 
 
 83 
 
 17.6 
 
 3 
 
 47520 
 
 54 
 
 81 
 
 108 
 
 18.6 
 
 3i 
 
 60417 
 
 69 
 
 103 
 
 137 
 
 19.7 
 
 &i 
 
 75460 
 
 86 
 
 129 
 
 172 
 
 20.7 
 
 81 
 
 92812 
 
 105 
 
 158 
 
 211 
 
 21.6 
 
 4 
 
 112640 
 
 128 
 
 192 
 
 256 
 
 22.6 
 
SHAFTING. 
 
 177 
 
 WORKING PROPORTIONS FOR CONTINUOUS 
 SHAFTING. 
 
 TRANSMITTING POWER, AND SUBJECT TO BENDING ACTION OP 
 PULLEYS, BELTING, ETC. 
 
 DIAMETER 
 OF SHAFT IN 
 INCHES. 
 
 MAX. SAFE TOR- 
 SIOVAL MOMENT 
 IN INCH-POUNDS. 
 
 REVOLUI 
 100 
 
 'IONS PER " 
 150 
 
 MINUTE. 
 200 
 
 MAX. DIS- 
 TANCE IN 
 FEET 
 
 BETWEEN 
 
 BEARINGS. 
 
 HP 
 
 IIP 
 
 HP 
 
 H 
 
 5940 
 
 5 
 
 7 
 
 10 
 
 6.8 
 
 If 
 
 7552 
 
 6 
 
 9 
 
 12 
 
 7.2 
 
 if 
 
 9432 
 
 8 
 
 11 
 
 15 
 
 7.5 
 
 if 
 
 11602 
 
 9 
 
 14 
 
 19 
 
 7.9 
 
 2 
 
 14080 
 
 11 
 
 17 
 
 23 
 
 8.2 
 
 w 
 
 16892 
 
 14 
 
 21 
 
 27 
 
 8.6 
 
 SH 
 
 20048 
 
 16 
 
 24 
 
 33 
 
 8.9 
 
 2| 
 
 23580 
 
 19 
 
 29 
 
 38 
 
 9.2 
 
 2* 
 
 27500 
 
 22 
 
 33 
 
 45 
 
 9 6 
 
 SI 
 
 36603 
 
 24 
 
 36 
 
 48 
 
 10.2 
 
 3 
 
 47520 
 
 39 
 
 58 
 
 77 
 
 10.8 
 
 3i 
 
 60417 
 
 49 
 
 74 
 
 98 
 
 11.4 
 
 8* 
 
 75460 
 
 61 
 
 92 
 
 123 
 
 12.0 
 
 3| 
 
 92812 
 
 75 
 
 113 
 
 151 
 
 12.5 
 
 4 
 
 112640 
 
 91 
 
 137 
 
 183 
 
 13.1 
 
 12 
 
178 AEEAS AND CIRCUMFERENCES OF CIRCLES. 
 
 TABLE OF CIRCLES. 
 
 Circumferences or areas intermediate of those in the table, may be found 
 by simple arithmetical proportion. The diameters, etc., are in inches ; but 
 it is plain that if the diameters are taken as feet, yards, etc., the other parts 
 will also be in those same measures. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMP. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 
 CUMP. 
 
 INS. 
 
 AREA. 
 BQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 164 
 
 .049087 
 
 .00019 
 
 1 15-16 
 
 6.P8684 
 
 2.9483 
 
 4 15-16 
 
 15.5116 
 
 19.147 
 
 1-32 
 
 .098175 
 
 .0 077 
 
 2. 
 
 6.28319 
 
 3.1416 
 
 5. 
 
 15.7080 
 
 19.635 
 
 3-64 
 
 .147262 
 
 .00173 
 
 1-16 
 
 6.47958 
 
 3.3410 
 
 1-16 
 
 15.9043 
 
 20.129 
 
 1-16 
 
 .196350 
 
 .00807 
 
 1-8 
 
 6.67588 
 
 3.5466 
 
 1-8 
 
 16.1007 
 
 20.629 
 
 332 
 
 .291524 
 
 .00690 
 
 3-16 
 
 6.87223 
 
 3.7583 
 
 3-16 
 
 16.2970 
 
 21.135 
 
 1-8 
 
 .3'.2699 
 
 .01227 
 
 1-4 
 
 7.06858 
 
 3.9761 
 
 1-4 
 
 16.4934 
 
 21.648 
 
 5-32 
 
 .4.90374 
 
 .01917 
 
 516 
 
 7.26493 
 
 4.2000 
 
 5-16 
 
 16.6S97 
 
 2-2.166 
 
 3-16 
 
 .589149 
 
 .02761 
 
 3-8 
 
 7.46128 
 
 4.4301 
 
 3-8 
 
 16.8861 
 
 22.691 
 
 7-32 
 
 .687223 
 
 .03758 
 
 7-16 
 
 7.65763 
 
 4.6664 
 
 7-16 
 
 17.C824 
 
 23.221 
 
 1-4 
 
 .7V5398 
 
 .04909 
 
 1-2 
 
 7.85398 
 
 4.9087 
 
 1-2 
 
 17.2788 
 
 23.758 
 
 9-32 
 
 .8^3573 
 
 .06213 
 
 9-16 
 
 8.05033 
 
 5.1572 
 
 9-16 
 
 17.4751 
 
 24.301 
 
 5-16 
 
 .981748 
 
 .07670 
 
 5-8 
 
 8.24U68 
 
 5.4119 
 
 5-S 
 
 17.6715 
 
 24.850 
 
 11-82 
 
 .07992 
 
 .09281 
 
 11-16 
 
 8.44303 
 
 5.6727 
 
 11-16 
 
 17.8678 
 
 25.406 
 
 3-8 
 
 .17810 
 
 .11045 
 
 3-4 
 
 8.68938 
 
 5.9896 
 
 3-4 
 
 18.0642 
 
 25.967 
 
 13-32 
 
 .27627 
 
 .12962 
 
 13-16 
 
 8.83573 
 
 6.2126 
 
 13-16 
 
 18.2605 
 
 26.535 
 
 7-16 
 
 .37445 
 
 .15033 
 
 7-8 
 
 9.032 8 
 
 6.4918 
 
 7-8 
 
 18.4569 
 
 27.109 
 
 15-32 
 
 .47262 
 
 .17257 
 
 15-: 6 
 
 9. 22*43 
 
 6.7771 
 
 15-16 
 
 18.6532 
 
 27.688 
 
 1,2 
 
 .57080 
 
 .19635 
 
 3. 
 
 9.42478 
 
 7.0686 
 
 6. 
 
 18.8496 
 
 28.274 
 
 17-32 
 
 .66897 
 
 .2-1166 
 
 1-^6 
 
 9.6-2113 
 
 7.8662 
 
 " '1-8 
 
 19.2423 
 
 29.465 
 
 9-16 
 
 .76715 
 
 .24850 
 
 1-8 
 
 9.81748 
 
 7.6699 
 
 l-l 
 
 19. (535!) 
 
 30.6SO 
 
 19-32 
 
 .86582 
 
 .27688 
 
 3-16 
 
 10.0138 
 
 7.9798 
 
 3-8 
 
 20.0277 
 
 31.919 
 
 5-8 
 
 .96350 
 
 .30:580 
 
 1-4 
 
 10.2102 
 
 s.2958 
 
 1-2 
 
 20.4204 
 
 33.183 
 
 21^32 
 
 2.061-67 
 
 .33824 
 
 5-16 
 
 10.4065 
 
 8.6179 
 
 5-8 
 
 20.8131 
 
 34.472 
 
 11-16 
 
 2.15984 
 
 .37122 
 
 3-8 
 
 10.6029 
 
 8.941)2 
 
 3-4 
 
 21.2058 
 
 3->.785 
 
 23-32 
 
 2.25802 
 
 .40574 
 
 7-16 
 
 10.7992 
 
 9.2806 
 
 7-8 
 
 21.5984 
 
 37.T22 
 
 3-4 
 
 2. .35619 
 
 .44179 
 
 1-2 
 
 10.9956 
 
 9.6211 
 
 7. 
 
 Ol Q(j 1 1 
 
 38.485 
 
 25-32 
 
 2.45487 
 
 .47937 
 
 9-16 
 
 11.1919 
 
 9.9678 
 
 1-8 
 
 22:3888 
 
 o9 871 
 
 13-16 
 
 2.55254 
 
 .51849 
 
 5-8 
 
 11.3883 
 
 10.321 
 
 1-4 
 
 22.7765 
 
 41.282 
 
 27-32 
 
 2.65072 
 
 .55914 
 
 11-16 
 
 11.1 5846 
 
 10.680 
 
 3-8 
 
 23.1692 
 
 42.718 
 
 7-8 
 
 2.74889 
 
 .60132 
 
 3-4 
 
 11.7810 
 
 11.045 
 
 1-2 
 
 23.5619 
 
 44.179 
 
 29-32 
 
 2.84707 
 
 .64504 
 
 13-16 
 
 11.9173 
 
 11.416 
 
 5-8 
 
 23.9546 
 
 45.664 
 
 15-Ki 
 
 2.! '4524 
 
 .69029 
 
 7-8 
 
 12.1737 
 
 11. 793 
 
 3-4 
 
 24.3473 
 
 47.173 
 
 31-32 
 
 3.04342 
 
 .73708 
 
 15-16 
 
 1-2.3700 
 
 12.177 
 
 7-8 
 
 24.7400 
 
 48.7'()7 
 
 1. 
 
 3.14159 
 
 .78540 
 
 4. 
 
 2.5664 
 
 12.566 
 
 8. 
 
 25.1327 
 
 50.265 
 
 1-16 
 
 3.33794 
 
 .88664 
 
 1-16 
 
 12.7627 
 
 12.<i62 
 
 1-8 
 
 25.5254 
 
 51.849 
 
 1-8 
 
 3.53429 
 
 .99402 
 
 1-8 
 
 2.9591 
 
 18.3K4 : 
 
 1-4 
 
 25.9181 
 
 53.456 
 
 3-16 
 
 3.73064 
 
 .1075 
 
 3-16 
 
 3.1554 
 
 13.772 
 
 3-8 
 
 26.3108 
 
 55.088 
 
 1-4 
 
 3.9*699 
 
 .2272 
 
 1-4 
 
 13.3518 
 
 14.186 
 
 1-2 
 
 26.7035 
 
 56.7'45 
 
 5-16 
 
 4.12334 
 
 .3530 
 
 5-16 
 
 3.5481 
 
 14.607 
 
 5-8 
 
 27.096-> 
 
 58.426 
 
 3-8 
 
 4.31969 
 
 .4849 
 
 3-8 
 
 3.744'> 
 
 15.033 
 
 3-4 
 
 27.4889; 
 
 60.132 
 
 7-16 
 
 4.51604 
 
 .62:50 
 
 7-16 
 
 3.9108 
 
 15.466 
 
 7-8 
 
 27.8816! 
 
 61.862 
 
 1-2 
 
 4.71239 
 
 .7671 
 
 1-2 
 
 4.1372 
 
 15.904 
 
 9. 
 
 28.2743 1 
 
 63.617 
 
 9-16 
 
 4.90874 
 
 .9175 
 
 9-11) 
 
 4.3335 
 
 16.349 
 
 1-8 
 
 28.6670: 
 
 65.397 
 
 5-8 
 
 5.1H509 
 
 2.0739 
 
 5-8 
 
 4.5299 
 
 16.800 
 
 1-4 
 
 29.0597 
 
 67.201 
 
 11-16 
 
 5.:-:Ol44 
 
 2.2365 
 
 11-16 
 
 4.7262 
 
 17.257 
 
 3-8 
 
 29.4524; 
 
 69. (129 
 
 3-4 
 
 5.49779 
 
 2.4053 
 
 34 
 
 4.92-26 
 
 17.721 
 
 1-2 
 
 29.84511 
 
 70.882 
 
 13-16 
 
 5.69414 
 
 2.5802 
 
 13-16 
 
 5.11K9 
 
 18.190 
 
 5-8 
 
 30. 2378 l 
 
 72.760 
 
 . 7-8 
 
 5.89049 
 
 2.7612 
 
 7-8 
 
 5.3153 
 
 18.665 
 
 3-4 
 
 30.6305 
 
 74.662 
 
AREAS AND CIRCUMFERENCES OF CIRCLES. 179 
 TABLE OF CIRCLES Continued. 
 
 DlAM. 
 
 INS. 
 
 Cm- 
 
 CUMF. 
 
 INS. 
 
 AREA. 
 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 9 7-8 
 
 31.0232 
 
 76.589 
 
 16 3-4 
 
 52.6217 
 
 220.35 
 
 23 5-8 
 
 74.2201 
 
 438.36 
 
 10. 
 
 31 .4159 
 
 78.540 
 
 7-8 
 
 53.0144 
 
 223.65 
 
 3-4 
 
 74.6128 443.01 
 
 1-8 
 
 31.8086 
 
 80.516 
 
 17. 
 
 53.4071 
 
 226.98 
 
 7-8 
 
 75.0055 447.69 
 
 1-4 
 
 32.2013 
 
 82.516 
 
 1-8 
 
 53.7998 
 
 230.33 
 
 21. 
 
 75.3982 452.39 
 
 3-8 
 
 32.5940 
 
 84.541 
 
 1-4 
 
 54.1925 
 
 233.71 
 
 1-8 
 
 75.7909 457.11 
 
 1-2 
 
 3-2.9867 
 
 86.590 
 
 3-8 
 
 54.5*52 
 
 237.10 
 
 1-4 
 
 76.1836 461.86 
 
 5-8 
 
 33.3794 
 
 88.664 
 
 1-2 
 
 54.9779 
 
 240.53 
 
 3-8 
 
 76.5763 466.64 
 
 3-4- 
 
 S3. 7721 
 
 90.763 
 
 5-8 
 
 55.3706 
 
 243.98 
 
 1-2 
 
 76.9690! 471.44 
 
 7-8 
 
 34.1648 
 
 92.886 
 
 3-4 
 
 55.7633 
 
 247.45 
 
 5-8 
 
 77.3617 476.26 
 
 11. 
 
 34.5575 
 
 95.033 
 
 7-8 
 
 56.1560 
 
 250.95 
 
 3-4 
 
 '77.7544 1 481.11 
 
 1-8 
 
 34.9502 
 
 97.205 
 
 18. 
 
 56.5487 
 
 254.47 
 
 7-8 
 
 78.1471 485.98 
 
 1-4 
 
 35.3429 
 
 99.402 
 
 1-8 
 
 56.9414 
 
 258.02 
 
 25. 
 
 78.5398 490.87 
 
 3-8 
 
 35.7356 
 
 101.62 
 
 1-4 
 
 57.3341 
 
 261 .59 
 
 1-8 
 
 78.9325 495.79 
 
 1-2 
 
 36.1283 
 
 103.87 
 
 3-8 
 
 57.7268 
 
 265.18 
 
 1-4 
 
 79.3252 500.74 
 
 5-8 
 
 36 5210 
 
 106.14 
 
 1-2 
 
 58.1195 
 
 268.80 
 
 3-8 
 
 79.7179 505.71 
 
 3-4 
 
 36.9137 
 
 108.43 
 
 5-8 
 
 58.5122 
 
 272.45 
 
 1-2 
 
 80.1106 510.71 
 
 7-8 
 
 37.3064 
 
 110.75 
 
 3-4 
 
 58.9049 
 
 276.12 
 
 5-8 
 
 80.5033 515.72 
 
 12. 
 
 37 6991 
 
 113.10 
 
 7-8 
 
 59.2976 
 
 279.81 
 
 3-4 
 
 80.8960 
 
 520.77 
 
 1-8 
 
 38.0918 
 
 115.47 
 
 19. 
 
 59.6903 
 
 283.53 
 
 7-8 
 
 81.2887 
 
 525.84 
 
 1-4 
 
 38.4845 
 
 117.86 
 
 1-8 
 
 60.0830 
 
 287.27 
 
 26. 
 
 81.6814 
 
 530.93 
 
 3-8 
 
 38.8772 
 
 120.28 
 
 1-4 
 
 60.4757 
 
 291.04 
 
 1-8 
 
 82.0741 536.05 
 
 1-2 
 
 39.2699 
 
 122.72 
 
 3-8 
 
 60.8684 
 
 294.83 
 
 1-4 
 
 82.4668 541.19- 
 
 5-8 
 
 39.6626 
 
 125.19 
 
 1-2 
 
 61.2611 
 
 298.65 
 
 3-8 
 
 82.8595 
 
 546.35 
 
 3-4 
 
 40.0553 
 
 127.68 
 
 5-8 
 
 61.6538 
 
 302.49 
 
 1-2 
 
 aS. 2522 
 
 551.55 
 
 7-8 
 
 40.4480 
 
 130.19 
 
 3-4 
 
 62.0465 
 
 3011.35 
 
 5-8 
 
 83.6449 
 
 556.76 
 
 13. 
 
 40.8407 
 
 132.73 
 
 7-8 
 
 62.4392 
 
 310.24 
 
 3-4 
 
 84.0376 
 
 562.00 
 
 1-8 
 
 41.2334 
 
 135.30 
 
 20. 
 
 62.8319 
 
 314.16 
 
 7-8 
 
 84.4303 567.27 
 
 1-4 
 
 41.6261 137.89 
 
 1-8 
 
 63.2246 
 
 318.10 
 
 27. 
 
 84.8230 
 
 572.56 
 
 3-8 
 
 42.0188 140.50 
 
 1-4 
 
 63.6173 
 
 322.06 
 
 1-8 
 
 85.2157 
 
 577.87 
 
 1-2 
 
 42.4115| 143.14 
 
 3-8 
 
 64.0100 
 
 326.05 
 
 1-4 
 
 85.6084 
 
 583.21 
 
 5-8 
 
 42.8042 145.80 
 
 1-2 
 
 64.4026 
 
 330. OH 
 
 3-8 
 
 86.0011 
 
 588.57 
 
 3-4 
 
 43.1969 
 
 148.49 
 
 5-8 
 
 64.7953 
 
 334.10 
 
 1-2 
 
 86.3938 593.96 
 
 7-8 
 
 43.5896 
 
 151.20 
 
 3-4 
 
 65.1880 
 
 338.16 
 
 5-8 
 
 86.7865! 599.37 
 
 14. 
 
 43.9823 
 
 153.94 
 
 7-8 
 
 65.5807 
 
 342.25 
 
 3-4 
 
 87.1792; 604.81 
 
 1-8 
 
 44.3750 
 
 156.70 
 
 21. 
 
 65.9734 
 
 346.36 
 
 7-8 
 
 87.5719 610.27 
 
 1-4 
 
 44.1677 
 
 159.48 
 
 1-8 
 
 66.3661 
 
 350.50 
 
 28. 
 
 87.9646 615.75 
 
 3-8 
 
 45.1604 
 
 162.30 
 
 1-4 
 
 66.7588 
 
 354.66 
 
 1-8 
 
 88.35731 6 1.26 
 
 1-2 
 
 45.5531 
 
 165.13 
 
 3-8 
 
 67.1515 
 
 358.84 
 
 1-4 
 
 88.7500 
 
 626.80 
 
 5-8 
 
 4*5.9458 
 
 167.99 
 
 1-2 
 
 67.5442 
 
 3(53.05 
 
 3-8 
 
 89.1427 
 
 632.36 
 
 3-4 
 
 46.3385 
 
 170.87 
 
 5-8 
 
 67.9369 
 
 367.28 
 
 1-2 
 
 89.5354 637.94 
 
 7-8 
 
 46.7312 
 
 173.78 
 
 3-4 
 
 68.3296 
 
 371.54 
 
 5-8 
 
 89.9281 643.55 
 
 15. 
 
 47.1239 
 
 176.71 
 
 7-8 
 
 68.7223 
 
 375. A3 
 
 3-4 
 
 90.3208' 649.18 
 
 1-8 
 
 47.5166 
 
 179.67 
 
 22. 
 
 69.1150! 380.13 
 
 7-8 
 
 90.7135j 654.84 
 
 1-4 
 
 47.9093 
 
 182.65 
 
 1-8 
 
 69.5077 
 
 384.46 
 
 29. 
 
 91.10621 660.52 
 
 3-8 
 
 48.3020 
 
 185.66 
 
 1-4 
 
 69.9004 
 
 388.82 
 
 1-8 
 
 91.4989 666.23 
 
 1-2 
 
 48.6947 
 
 188.69 
 
 3-8 
 
 70.2931 
 
 393.20 
 
 1-4 
 
 91.8916' 671.96 
 
 5-8 
 
 49.0874 
 
 191.75 
 
 1-2 
 
 70.6858 
 
 397.61 
 
 3-8 
 
 92.2843 677.71 
 
 3-4 
 
 49.4801 
 
 194.83 
 
 5-8 
 
 71.0785 
 
 402.04 
 
 1-2 
 
 92.6770 683.49 
 
 7-8 
 
 49.8728 
 
 197.93 
 
 3-4 
 
 71.4712 
 
 406.49 
 
 5-8 
 
 93.0697 689.30 
 
 16. 
 
 50.2655 
 
 201.06 
 
 7-8 
 
 71.8889 
 
 410.97 
 
 34 
 
 93.4624 
 
 695.13 
 
 1-8 
 
 50.6582 
 
 204.22 
 
 23. 
 
 72.2566 
 
 415.48 
 
 7-8 
 
 93.8551 
 
 700.98 
 
 1-4 
 
 51.0509 
 
 207.39 
 
 1-8 
 
 72.6493 
 
 420.00 
 
 30. 
 
 94.2478 706.86 
 
 3-8 
 
 51.4436 
 
 210.60 
 
 1-4 
 
 73.0420 
 
 424.56 
 
 18 
 
 94.6405 712.76 
 
 1-2 
 
 51.8363 
 
 213.82 
 
 3-8 
 
 73.4347 
 
 429.13 
 
 1-4 
 
 95.0332 
 
 718.69 
 
 5-8 
 
 52.2290 
 
 217.08 
 
 1-2 
 
 73.8274 
 
 433.74 
 
 3-8 
 
 95.4259 
 
 724.64 
 
180 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 TABLE OF CIRCLES Continued. 
 
 DlAM. 
 
 INS. 
 
 CIR- 
 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 CIR- 
 
 CTJMF. 
 
 INS. 
 
 ARE*. 
 SQ. INS. 
 
 30 1-2 
 
 95.8186 
 
 730.62 
 
 37 3-8 
 
 117.417 
 
 1097.1 
 
 44 1-4 
 
 139.015 
 
 1537.9 
 
 5-8 
 
 96.21131 736.62 
 
 1-2 
 
 117.810 
 
 1104.5 
 
 3-8 
 
 139.408 
 
 1546.6 
 
 3-4 
 
 96.6040 742.64 
 
 5-8 
 
 118.202 
 
 1111.8 
 
 1-2 
 
 139.801 
 
 1555.3 
 
 7-8 
 
 96.9967 748.69 
 
 3-4 
 
 118.596 
 
 1119.2 
 
 5-8 
 
 140.194 
 
 1564.0 
 
 31. 
 
 97.3894! 754 .-77 
 
 7-8 
 
 118.988 
 
 1126.7 
 
 3-4 
 
 140.586 
 
 1572.8 
 
 18 
 
 97.7821 760.87 
 
 38. 
 
 119.381 
 
 1134.1 
 
 7-8 
 
 140.979 
 
 1581.6 
 
 1-4 
 
 98.1748 766.99 
 
 1-8 
 
 119.773 
 
 1141.6 
 
 45. 
 
 141.372 
 
 1590.4 
 
 3-8 
 
 98.5675 
 
 773.14 
 
 1-4 
 
 120.166 
 
 1149.1 
 
 1-8 
 
 141.764 
 
 1599.3 
 
 1-2 
 
 98.9602 
 
 779.31 
 
 3-8 
 
 120.559 
 
 1156.6 
 
 1-4 
 
 142.157 
 
 1608.2 
 
 5-8 
 
 99.3529 
 
 785.51 
 
 1-2 
 
 1*0.951 
 
 1164.2 
 
 3-8 
 
 142.550 
 
 1617.0 
 
 3-4 
 
 99.7456 
 
 791.73 
 
 5-8 
 
 121.344 
 
 1171.7 
 
 1-2 
 
 142.942 
 
 1626.0 
 
 7-8 
 
 100.138 
 
 797.98 
 
 3-4 
 
 121.737 
 
 1179.3 
 
 5-8 
 
 143.335 
 
 1634.9 
 
 32. 
 
 100.531 
 
 804.25 
 
 7-8 
 
 122.129 
 
 1186.9 
 
 3-4 
 
 143.728 
 
 1643.9 
 
 1-8 
 
 100.924 
 
 810.54 
 
 39. 
 
 122.522 
 
 1194.6 
 
 7-8 
 
 144.121 
 
 1652.9 
 
 1-4 
 
 101.316 
 
 816.86 
 
 1-8 
 
 122.915 
 
 1202.3 
 
 46. 
 
 144.513 
 
 1661.9 
 
 3-8 
 
 101.709 
 
 823.21 
 
 1-4 
 
 123.308 
 
 1210.0 
 
 1-8 
 
 144.906 
 
 1670.9 
 
 1-2 
 
 102.102 
 
 829.58 
 
 3-8 
 
 123.700 
 
 1217.7 
 
 1-4 
 
 145.299 
 
 1680.0 
 
 5-8 
 
 102.494 
 
 835.97 
 
 1-2 
 
 124.093 
 
 1225.4 
 
 3-8 
 
 145.691 
 
 1689.1 
 
 3-4 
 
 102.887 
 
 842.39 
 
 5-8 
 
 124.486 
 
 1233.2 
 
 1-2 
 
 146.084 
 
 1698.2 
 
 7-8 
 
 103.280 
 
 848.83 
 
 3-4 
 
 124.878 
 
 1241.0 
 
 5-8 
 
 146.477 
 
 1707.4 
 
 33. 
 
 103.673 
 
 855.30 
 
 7-8 
 
 125.271 
 
 1248.8 
 
 3-4 
 
 146.869 
 
 1716.5 
 
 1-8 
 
 104.065 
 
 861.79 
 
 46. 
 
 125.664 
 
 1256.6 
 
 7-8 
 
 147.262 
 
 17'25.7 
 
 1-4 
 
 104.458 
 
 868.31 
 
 1-8 
 
 126.056 
 
 1264.5 
 
 47. 
 
 147.655 
 
 1734.9 
 
 3-8 
 
 104.851 
 
 874.85 
 
 1-4 
 
 126.449 
 
 1272 .4 
 
 1-8 
 
 148.048 
 
 1744.2 
 
 1-2 
 
 105.243 
 
 881.41 
 
 3-8 
 
 126.842 
 
 1280.3 
 
 1-4 
 
 148.440 
 
 1753.5 
 
 5-8 
 
 105.636 
 
 888.00 
 
 1-2 
 
 127.2% 
 
 1288.2 
 
 3-8 
 
 148.8^3 
 
 1762.7 
 
 3-4 
 
 106.029 
 
 894.62 
 
 5-8 
 
 127.627 
 
 1296.2 
 
 1-2 
 
 149.226 
 
 1772.1 
 
 7-8 
 
 106.421 
 
 901 .26 
 
 f-4 
 
 128.020 
 
 1S04.2 
 
 5-8 
 
 149.618 
 
 1781.4 
 
 34. 
 
 106.814 
 
 907.92 
 
 7-8 
 
 128.413 
 
 1312.2 
 
 3-4 
 
 150.011 
 
 1790.8 
 
 1-8 
 
 107.207 
 
 914.61 
 
 41. 
 
 128.805 
 
 1320.3 
 
 7-8 
 
 150.404 
 
 1800.1 
 
 1-4 
 
 107.600 
 
 921.32 
 
 1-8 
 
 129.198 
 
 1328.3 
 
 48. 
 
 150.796 
 
 1809.6 
 
 3-8 
 
 107.992 
 
 928.06 
 
 1-4 
 
 129.591 
 
 1336.4 
 
 1-8 
 
 151.189 
 
 1819.0 
 
 12 
 
 108.385 
 
 934.82 
 
 3-8 
 
 129.993 
 
 1344.5 
 
 1-4 
 
 151.582 
 
 1828.5 
 
 5-8 
 
 108.778 
 
 941.61 
 
 1-2 
 
 130.376 
 
 1352.7 
 
 3,8 
 
 151.975 
 
 1837.9 
 
 3-4 
 
 109.170 
 
 948.42 
 
 5-8 
 
 130.769 
 
 1360.8 
 
 1-2 
 
 152.367 
 
 1847.5 
 
 7-8 
 
 109.563 
 
 955.25 
 
 34 
 
 131.161 
 
 1369.0 
 
 5-8 
 
 152.760 
 
 1&57.0 
 
 35. 
 
 109.956 
 
 962.11 
 
 7-8 
 
 131.554 
 
 1377.2 
 
 3-4 
 
 153.153 
 
 1866.5 
 
 1-8 
 
 110.348 
 
 969.00 
 
 4ft. 
 
 131.947 
 
 1385.4 
 
 7-8 
 
 153.545 
 
 1876.1 
 
 1-4 
 
 110.741 
 
 975.91 
 
 1-8 
 
 132.340 
 
 1393.7 
 
 49. 
 
 153.938 
 
 1885.7 
 
 3-8 
 
 111.134 
 
 982.84 
 
 1-4 
 
 132.732 
 
 1402.0 
 
 1-8 
 
 154.881 1895.4 
 
 1-2 
 
 111.527 
 
 989.80 
 
 3-8 
 
 133.125 
 
 1410.3 
 
 1-4 
 
 154.723 
 
 1905.0 
 
 5-8 
 
 111.919 
 
 996.78 
 
 1-2 
 
 133.518 
 
 1418.6 
 
 3-8 
 
 155.116 
 
 1914.7 
 
 3-4 
 
 112.312 
 
 1003.8 
 
 5-8 
 
 133.910 
 
 1427.0 
 
 1-2 
 
 155.509 
 
 1924.4 
 
 7-8 
 
 112.705 
 
 1010.8 
 
 3-4 
 
 134.303 
 
 1435.4 
 
 5-8 
 
 155.902 
 
 1934.2 
 
 36. 
 
 113.097 
 
 1017.9 
 
 7-8 
 
 134. K96 
 
 1443.8 
 
 3-4 
 
 156.294 
 
 1943.9 
 
 1-8 
 
 113.490 
 
 1025.0 
 
 43. 
 
 135.088 
 
 1452.2 
 
 7-8 
 
 156.687 
 
 1953.7 
 
 1-4 
 
 113.883 
 
 1032.1 
 
 1-8 
 
 135.481 
 
 1460.7 
 
 50. 
 
 157.080 
 
 1963.5 
 
 3-8 
 
 114.275 
 
 1039.2 
 
 1-4 
 
 135.874 
 
 1469.1 
 
 1-8 
 
 157.472 1W3.3 
 
 1-2 
 
 114.668 
 
 1046.3 
 
 3-8 
 
 136.267 
 
 1477.6 
 
 , 1-4 
 
 157.865 
 
 1983.2 
 
 5-8 
 
 115.061 
 
 1053.5 
 
 1-2 
 
 136.659 
 
 1486.2 
 
 3-8 
 
 158.258 
 
 1993.1 
 
 3-4 
 
 115.454 
 
 1060.7 
 
 5-8 
 
 137.052 
 
 1494.7 
 
 1-2 
 
 158.650 
 
 2003.0 
 
 7-8 
 
 115.846 
 
 1068.0 
 
 3-4 
 
 137.445 
 
 1503.3 
 
 5-8 
 
 159.043 
 
 2012.9 
 
 37. 
 
 116.239 
 
 1075.2 
 
 7-8 
 
 137.837 
 
 1511.9 
 
 3-4 
 
 159.436 
 
 2022.8 
 
 1-8 
 
 116.632 
 
 1082.5 
 
 44. 
 
 138.230 
 
 1520.5 
 
 7-8 
 
 159.829 
 
 2032.8 
 
 1-4 
 
 117.024 
 
 1089.8 
 
 1-8 
 
 138.623 
 
 1529.2 
 
 51. 
 
 160.221 
 
 2042.8 
 
ABEAS AND CIRCUMFERENCES OF CIRCLES. 181 
 TABLE OF CIRCLES Continued. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 
 CUMP. 
 
 INS. 
 
 ARKA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 CIR- 
 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 51 1-8 
 
 160.614 
 
 2052.8 
 
 58. 
 
 182.212 
 
 2642.1 
 
 64 7-8 
 
 203.811 
 
 3305.6 
 
 1-4 
 
 161.007 
 
 2062.9 
 
 1-8 
 
 182.605 
 
 2653.5 
 
 65. 
 
 204.204 
 
 3318.3 
 
 3-8 
 
 161.399 
 
 2073.0 
 
 1-4 
 
 182.998 
 
 2664.9 
 
 1-8 
 
 204.596 
 
 3331.1 
 
 1-2 
 
 161.792 
 
 2083.1 
 
 3-8 
 
 183.390 
 
 2676.4 
 
 1-4 
 
 204.989 
 
 3343.9 
 
 5-8 
 
 162.18-. 
 
 2093.2 
 
 1-2 
 
 183.783 
 
 2687.8 
 
 3-8 
 
 205.382 
 
 3356.7 
 
 3-4 
 
 162.577 
 
 2103.3 
 
 5-8 
 
 184.176 
 
 2699.3 
 
 1-2 
 
 205.774 
 
 3369.6 
 
 7-8 
 
 162.970 
 
 2113.5 
 
 3-4 
 
 184.569 
 
 2710.9 
 
 5-8 
 
 206.167 
 
 3382.4 
 
 52. 
 
 163.363 
 
 2123.7 
 
 7-8 
 
 184.961 
 
 2722.4 
 
 3-4 
 
 206.560 
 
 3395.3 
 
 1-8 
 
 163.756 
 
 2133.9 
 
 59. 
 
 185.354 
 
 2734.0 
 
 7-8 
 
 2- 6.952 
 
 3408.2 
 
 1-4 
 
 164. 14S 
 
 2144.2 
 
 1-8 
 
 185.747 
 
 2745.6 
 
 66. 
 
 207.345 
 
 3421.2 
 
 3-8 
 
 164.541 
 
 2154.5 
 
 1-4 
 
 186.139 
 
 2757.2 
 
 1-8 
 
 207.738 
 
 3434.2 
 
 1-2 
 
 164.934 
 
 2164.8 
 
 3-8 
 
 186.532 
 
 2768.8 
 
 1-4 
 
 208.131 
 
 3447.2 
 
 5-8 
 
 165.336 
 
 2175.1 
 
 1-2 
 
 186.925 
 
 2780.5 
 
 3-8 
 
 208.523 
 
 3460.2 
 
 3-4 
 
 165.719 
 
 2!85.4 
 
 5-8 
 
 187.31? 
 
 2792.2 
 
 1-2 
 
 208.916 
 
 3473.2 
 
 7-8 
 
 166.112 
 
 2195.8 
 
 3-4 
 
 187.7KI 
 
 2803.9 
 
 5-8 
 
 209.309 
 
 3486.3 
 
 53. 
 
 166.504 
 
 2203.2 
 
 7-8 
 
 188.103 
 
 2815.7 
 
 3-4 
 
 209.701 
 
 3499.4 
 
 1-8 
 
 166.897 
 
 2216.6 
 
 60. 
 
 188.496 
 
 2827.4 
 
 7-8 
 
 210. ('94 
 
 a512.5 
 
 1-4 
 
 167.290 
 
 2227.0 
 
 1-8 
 
 188.888 
 
 2839.2 
 
 67. 
 
 210.487 
 
 3525.7 
 
 3-8 
 
 167.683 
 
 2237.5 
 
 1-4 
 
 189.281 
 
 2851.0 
 
 1-8 
 
 210.879 
 
 b538.8 
 
 1-2 
 
 168.075 
 
 2248.0 
 
 3-8 
 
 189 674 
 
 2862.9 
 
 1-4 
 
 211.272 
 
 3552.0 
 
 5-8 
 
 168.468 
 
 2253.5 
 
 1-2 
 
 190.066 
 
 2874.8 
 
 3-8 
 
 211.665 
 
 a565.2 
 
 3-4 
 
 168.861 
 
 22(39.1 
 
 5-8 
 
 191.459 
 
 2S86.6 
 
 1-2 
 
 212.058 
 
 3578.5 
 
 7-8 
 
 169.253 
 
 2279.6 
 
 3-4 
 
 190.852 
 
 2898.6 
 
 5-8 
 
 212.450 
 
 3.391.7 
 
 54. 
 
 169.646 
 
 2290 2 
 
 7-8 
 
 191.244 
 
 2910.5 
 
 3-4 
 
 212.843 
 
 3605.0 
 
 1-8 
 
 170.039 
 
 2300.8 
 
 61. 
 
 191.6*7 
 
 2922.5 
 
 7-8 
 
 213.236 
 
 3618.3 
 
 1-4 
 
 170.431 
 
 2311.5 
 
 1-8 
 
 192.030 
 
 2934.5 
 
 68. 
 
 213.628 
 
 3631.7 
 
 3-8 
 
 170.824 
 
 2322.1 
 
 1-4 
 
 192.423 
 
 2916.5 
 
 1-8 
 
 214.021 
 
 3645.0 
 
 1-2 
 
 171.217 
 
 2332.8 
 
 3-8 
 
 192.815 
 
 2958.5 
 
 1-4 
 
 214.414 
 
 3658.4 
 
 5-8 
 
 171.609 
 
 2343.5 
 
 1-2 
 
 193. 20s 
 
 2970.6 
 
 3-8 
 
 214.806 
 
 3671.8 
 
 3-4 
 
 172.002 
 
 2354.3 
 
 5-8 
 
 193.601 
 
 2982.7 
 
 1-2 
 
 215.199 
 
 3685.3 
 
 7-8 
 
 172. &95 
 
 2365.0 
 
 3-4 
 
 193.993 
 
 5994. 8 
 
 5-8 
 
 215.592 
 
 3698.7 
 
 55. 
 
 172.788 
 
 2375.8 
 
 7-8 
 
 194.388 
 
 3006 9 
 
 3-4 
 
 215.984 
 
 3712.2 
 
 1-8 
 
 173.180 
 
 2386.6 
 
 62. 
 
 194.779 
 
 3(119.1 
 
 7-8 
 
 216.377 
 
 3725.7 
 
 1-4 
 
 173.573 
 
 2397.5 
 
 1-8 
 
 195.171 
 
 3031.3 
 
 69. 
 
 216.770 
 
 3789.3 
 
 3-8 
 
 173.966 
 
 2108.3 
 
 1-4 
 
 195.564 
 
 3043.5 
 
 1-8 
 
 217. 163 
 
 3752.8 
 
 1-2 
 
 174.358 
 
 2419.2 
 
 3-8 
 
 195.957 
 
 3055.7 
 
 1-4 
 
 217.555 
 
 3766.4 
 
 5-8 
 
 174.751 
 
 24:30.1 
 
 1-2 
 
 196.350 
 
 3068.0 
 
 38 
 
 217.948 
 
 3780.0 
 
 3-4 
 
 175.144 
 
 2441 .1 
 
 5-8 
 
 196.742 
 
 3080.3 
 
 1-2 
 
 218.341 
 
 3793.7 
 
 7-8 
 
 175.536 
 
 2452.0 
 
 3-4 
 
 197.135 
 
 3092.6 
 
 5-8 
 
 218.733 
 
 3807.3 
 
 56. 
 
 175.929 
 
 2463.0 
 
 7-8 
 
 197.528 
 
 3104.9 
 
 3-4 
 
 219.126 
 
 3821.0 
 
 1-8 
 
 176.3-22 
 
 2474.0 
 
 63. 
 
 197.920 
 
 3117.2 
 
 7-8 
 
 219.519 
 
 3834.7 
 
 1-4 
 
 176.715 
 
 2485.0 
 
 1-8 
 
 198.313 
 
 3129.6 
 
 70. 
 
 219.911 
 
 3H48.5 
 
 3-8 
 
 177.107 
 
 2496.1 
 
 1-4 
 
 198.706 
 
 3142.0 
 
 1-8 
 
 220.304 
 
 3862.2 
 
 1-2 
 
 177.500 
 
 2507.2 
 
 3-8 
 
 199.098 
 
 3154.5 
 
 1-4 
 
 220.697 
 
 3876.0 
 
 5-8 
 
 177.893 
 
 2518.3 
 
 1-2 
 
 199.491 
 
 3166.9 
 
 3-8 
 
 221.000 
 
 3889.8 
 
 3-4 
 
 178.285 
 
 2529.4 
 
 5-8 
 
 199.884 
 
 3179.4 
 
 1-2 
 
 221.482 
 
 3903.6 
 
 7-8 
 
 178.678 
 
 2540.6 
 
 3-4 
 
 200.277 
 
 3191.9 
 
 5-8 
 
 221.875 
 
 3917.5 
 
 57. 
 
 179.071 
 
 2551.8 
 
 7-8 
 
 200.669 
 
 3204.4 
 
 3-4 
 
 222.268 
 
 3931.4 
 
 1-8 
 
 179.463 
 
 2563.0 
 
 61. 
 
 201.062 
 
 3-217.0 
 
 7-8 
 
 222.660 
 
 3945.3 
 
 1-4 
 
 179.856 
 
 2574.2 
 
 1-8 
 
 201.455 
 
 3229.6 
 
 71. 
 
 223.053 
 
 3959.2 
 
 3-8 
 
 180.249 
 
 2585.4 
 
 1-4 
 
 201.847 
 
 3242.2 
 
 1-8 
 
 223.446 
 
 3973.1 
 
 1-2 
 
 180.642 
 
 2596.7 
 
 3-8 
 
 202.240 
 
 3254.8 
 
 1-4 
 
 223.838 
 
 3987.1 
 
 5-8 
 
 181 .034 
 
 2608.0 
 
 1-2 
 
 202.633 
 
 3267.5 
 
 3-8 
 
 224.231 
 
 4001.1 
 
 3-4 
 
 181.427 
 
 2619.4 
 
 5-8 
 
 203.025 
 
 3280.1 
 
 1-2 
 
 224.624 
 
 4015.2 
 
 7-8 
 
 181.820 
 
 2630.7 
 
 3-4 
 
 203.418 
 
 3292.8 
 
 5-8 
 
 225.017 
 
 4029.2 
 
182 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 TABLE OF CIRCLES Continued. 
 
 DlAM. 
 
 INS. 
 
 ClB- 
 
 CUMP. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMP. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 713-4 
 
 225.409 
 
 4043.3 
 
 78 5-8 
 
 247.008 
 
 4855.2 
 
 85 1-2 
 
 268.606 
 
 5741.5 
 
 7-8 
 
 225.802 4057.4 
 
 3-4 
 
 247.400 
 
 4870.7 
 
 5-8 
 
 268.999 
 
 5758.3 
 
 72. 
 
 226.195 4071.5 
 
 7-8 
 
 247.793 
 
 4886.2 
 
 3-4 
 
 269.392 
 
 5775.1 
 
 1-8 
 
 226.587 
 
 4085.7 
 
 79. 
 
 248.186 
 
 4901.7 
 
 7-8 
 
 269.784 
 
 5791 .9 
 
 1-4 
 
 226.980 
 
 4099.8 
 
 1-8 
 
 248.579 
 
 4917.2 
 
 86. 
 
 270.177 
 
 5808.8 
 
 3-8 
 
 227.373 4114.0 
 
 1-4 
 
 248.971 
 
 4932.7 
 
 1-8 
 
 270.570 
 
 5825.7 
 
 1-2 
 
 227.765 
 
 4128.2 
 
 3-8 
 
 249.364 
 
 4948.3 
 
 1-4 
 
 270.962 
 
 5842.6 
 
 5-8 
 
 228.158 
 
 4142.5 
 
 1-2 
 
 249.757 
 
 4963.9 
 
 3-8 
 
 271.1355 
 
 5859.6 
 
 3-4 
 
 828.551 
 
 4156.8 
 
 5-8 
 
 250.149 
 
 4979.5 
 
 1-2 
 
 271.748 
 
 5876.5 
 
 7-8 
 
 228 9441 4171.1 
 
 3-4 
 
 250.542 
 
 4995.2 
 
 5-8 
 
 272.140 
 
 5893.5 
 
 73. 
 
 229. a36 
 
 4185.4 
 
 7-8 
 
 250.935! 5010.9 
 
 3-4 
 
 272.533 
 
 5910.6 
 
 1-8 
 
 229.729 
 
 4199.7 
 
 80. 
 
 251. 327 i 5026.5 
 
 7-8 
 
 272.926 
 
 5927.6 
 
 1-4 
 
 230.122 
 
 4214.1 
 
 1-8 
 
 25l.720| 5042.3 
 
 87. 
 
 273.319 
 
 5944.7 
 
 3-8 
 
 230.514 
 
 4228.5 
 
 1-4 
 
 252.113 5058.0 
 
 1-8 
 
 273.711 
 
 5961.8 
 
 1-2 
 
 230.907 
 
 4242.9 
 
 3-8 
 
 252.506 5073.8 
 
 1-4 
 
 274.104 
 
 5978.9 
 
 5-8 
 
 231.300 
 
 4257.4 
 
 1-2 
 
 252.898 5089.6 
 
 3-8 
 
 274.497 5996.0 
 
 3-4 
 
 231.692 
 
 4271.8 
 
 5-8 
 
 253.291 5105.4 
 
 1-2 
 
 274.889 6013.2 
 
 7-8 
 
 232.085 
 
 4286.3 
 
 3-4 
 
 253.684 5121.2 
 
 5-8 
 
 275.282 6030.4 
 
 74. 
 
 232.478 
 
 4300.8 
 
 7-8 
 
 254.076 
 
 5137.1 
 
 3-4 
 
 275.675 6047.6 
 
 1-8 
 
 232.871 
 
 4315.4 
 
 81. 
 
 254.469 
 
 5153.0 
 
 7-8 
 
 276.067 
 
 6064.9 
 
 1-4 
 
 233 263 
 
 4329.9 
 
 1-8 
 
 254.862 
 
 5168.9 
 
 88. 
 
 276.460 
 
 6082.1 
 
 3-8 
 
 233.656 
 
 4:i44.5 
 
 1-4 
 
 255.254 5184.9 
 
 1-8 
 
 276.853! 6099.4 
 
 1-2 
 
 234.049 
 
 4359.2 
 
 3-8 
 
 255.647 5200.8 
 
 1-4 
 
 277.246! 6116.7 
 
 5-8 
 
 234.441 
 
 4373.8 
 
 1-2 
 
 256.0401 5216.8 
 
 3-8 
 
 277.638 
 
 6134.1 
 
 3-4 
 
 234.834 
 
 4388.5 
 
 5-8 
 
 256.433! 5232.8 
 
 1-2 
 
 278.031 
 
 6151.4 
 
 7-8 
 
 235.2271 4403.1 
 
 3-4 
 
 256.8251 5248.9 
 
 5-8 
 
 278.424 
 
 6168.8 
 
 75. 
 
 235.619 
 
 4417.9 
 
 7-8 
 
 257.218! 5264.9 
 
 3-4 
 
 278.816 
 
 6186.2 
 
 1-8 
 
 236.012 
 
 4432.6 
 
 82. 
 
 257.6111 5281.0 
 
 7-8 
 
 279.209 
 
 6203.7 
 
 1-4 
 
 236.405 4447.4 
 
 1-8 
 
 258.003 
 
 5297.1 
 
 89. 
 
 279.602 
 
 6221.1 
 
 3-8 
 
 236.798 4462.2 
 
 1-4 
 
 258.396 
 
 5313.3 
 
 1-8 
 
 279.994 
 
 6238.6 
 
 1-2 
 
 237.190| 4477.0 
 
 3-8 
 
 258.789 
 
 5329.4 
 
 1-4 
 
 280.387 
 
 6256.1 
 
 5-8 
 
 237.583! 4491.8 
 
 1-2 
 
 259.181 
 
 5345.6 
 
 3-8 
 
 280.780 
 
 6273.7 
 
 3-4 
 
 237.976! 4506.7 
 
 5-8 
 
 259.574 
 
 5361.8 
 
 1-2 
 
 281.173 
 
 6291.2 
 
 7-8 
 
 238.368 4521.5 
 
 3-4 
 
 259.967 
 
 5378.1 
 
 5-8 
 
 281.565 
 
 6308.8 
 
 76. 
 
 2:.761 
 
 4536.5 
 
 7-8 
 
 260.359 
 
 5394.3 
 
 3-4 
 
 281.958 
 
 6326.4 
 
 1-8 
 
 239.154 
 
 4551.4 
 
 83. 
 
 260.752 
 
 5410.6 
 
 7-8 
 
 282.351 
 
 6344.1 
 
 1-4 
 
 239.546 4566.4 
 
 1-8 
 
 261.145 
 
 5426.9 
 
 90. 
 
 282.743 
 
 6361.7 
 
 3-8 
 
 239.939 4581.3 
 
 1-4 
 
 261.538 
 
 5443.3 
 
 1-8 
 
 283.136 
 
 6379.4 
 
 1-2 
 
 240.332 4596.3 
 
 3-8 
 
 261.930 
 
 5459.6 
 
 1-4 
 
 283.529 
 
 6397.1 
 
 5-8 
 
 240.725 4611.4 
 
 1-2 
 
 262.323 
 
 5476.0 
 
 3-8 
 
 283.921 
 
 6414.9 
 
 3-4 
 
 241.1171 4626.4 
 
 5-8 
 
 262.716 
 
 5492.4 
 
 1-2 
 
 284.314 
 
 6432.6 
 
 7-8 
 
 241.510! 4641.5 
 
 3-4 
 
 263.108 
 
 5508.8 
 
 5-8 
 
 284.707 
 
 6450.4 
 
 77. 
 
 241.903: 4656.6 
 
 7-8 
 
 263.501 
 
 5525.3 
 
 3-4 
 
 285.100 
 
 6468.2 
 
 1-8 
 
 242.295J 4671.8 
 
 84. 
 
 263.894 
 
 5541 .8 
 
 7-8 
 
 285.492 
 
 6486.0 
 
 1-4 
 
 242.688 4686.9 
 
 1-8 
 
 264.286 
 
 5558.3 
 
 91. 
 
 285.885 
 
 6503.9 
 
 3-8 
 
 243.081 4702.1 
 
 1-4 
 
 264.679 
 
 5574.8 
 
 1-8 
 
 286.278 
 
 6521.8 
 
 1-2 
 
 243.473 4717.3 
 
 3-8 
 
 265.072 
 
 5591.4 
 
 1-4 
 
 286.670 
 
 6539.7 
 
 5-8 
 
 243.866: 4732.5 
 
 1-2 
 
 265.465 
 
 5K07.9 
 
 3-8 
 
 287.063 
 
 6557.6 
 
 3-4 
 
 244.259! 4747.8 
 
 5-8 
 
 265.857 
 
 5K24.5 
 
 1-2 
 
 287.456 
 
 6575.5 
 
 7-8 
 
 244.652 4763.1 
 
 3-4 
 
 266.250 
 
 5641.2 
 
 5-8 
 
 287.848 
 
 6593.5 
 
 78. 
 
 245.044! 4778.4 
 
 7-8 
 
 266.643 
 
 5657.8 
 
 3-4 
 
 288.241 
 
 6611.5 
 
 1-8 
 
 245.437 4798.7 
 
 85. 
 
 267.035 
 
 5674.5 
 
 7-8 
 
 288. 634 
 
 6(i29.6 
 
 1-4 
 
 245.830 4809.0 
 
 1-8 
 
 267.428 
 
 5691.2 
 
 92. 
 
 289.027 
 
 6647.6 
 
 3-8 
 
 246.222 
 
 4824.4 
 
 14 
 
 267.821 
 
 5707.9 
 
 1-8 
 
 289.419 
 
 6665.7 
 
 1-2 
 
 246.615 
 
 4839.8 
 
 3-8 
 
 268.213 
 
 5724.7 
 
 1-4 
 
 289.812 
 
 6683.8 
 
AKEAS AND CIKCUMFERENCES OF CIECLES. 183 
 TABLE OF CIRCLES Continued. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMF. 
 
 INS. 
 
 AREA. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 ClR- 
 CUMF. 
 
 INS. 
 
 ABE A. 
 SQ. INS. 
 
 DlAM. 
 
 INS. 
 
 Cm- 
 
 CUMF. 
 
 INS. 
 
 A"KA. 
 
 SQ. INS. 
 
 92 3-8 
 
 290.205 
 
 6701.9 
 
 95. 
 
 298.451 
 
 7088.2 
 
 97 5-8 
 
 306.698 
 
 7485.8 
 
 1-2 
 
 290.597 
 
 6720.1 
 
 1-8 
 
 298.844 7106.9 
 
 3-4 
 
 307.091 7504.5 
 
 5-8 
 
 290.990 
 
 6738.2 
 
 1-4 
 
 299.237 7125.6 
 
 7-8 
 
 807.468 7523.7 
 
 3-4 
 
 291.383 
 
 6756.4 
 
 3-8 
 
 299,629 7144.3 
 
 98. 
 
 307.876 7543.0 
 
 7-8 
 
 291.775 
 
 6774.7 
 
 1-2 
 
 300.022 716::. 
 
 1-8 
 
 308.269 7562.2 
 
 93. 
 
 292.168 
 
 6792.9 
 
 5-8 
 
 300.415 7181.8 
 
 1-4 
 
 308.661 7581.5 
 
 1-8 
 
 292.561 
 
 6811.2 
 
 3-4 
 
 800.807 7-J00.6 
 
 3-8 
 
 309.054 
 
 7600.8 
 
 1-4 
 
 292.954 
 
 6829.5 
 
 7-8 
 
 301. 200 : 7219.4 
 
 1-2 
 
 309.447 
 
 7620.1 
 
 3-8 
 
 293.346 
 
 6847.8 
 
 96. 
 
 301.593 7238.2 
 
 5-8 
 
 809.840 7639.5 
 
 1-2 
 
 293.739 
 
 6866.1 
 
 1-8 
 
 301.986 
 
 7257.1 
 
 3-4 
 
 310.232 7658.9 
 
 5-8 
 
 294.132 
 
 6884.5 
 
 1-4 
 
 302.3781 7276.0 
 
 7-8 
 
 310.625 7678.3 
 
 3-4 
 
 294.524 
 
 6902.9 
 
 3-8 
 
 302.771 7294.9 
 
 199. 
 
 311.018 7697.7 
 
 7-8 
 
 294.917 
 
 6921.3 
 
 1-2 
 
 303.1 64 7313.8 
 
 1-8 
 
 311.410 7717.1 
 
 M. 
 
 295.310 
 
 6939.8 
 
 5-8 
 
 303.556- 7332.8 
 
 1-4 
 
 311.803! 7736.6 
 
 1-8 
 
 295.702 
 
 6958.2 
 
 3-4 
 
 303.949 7351.8 
 
 3-8 
 
 312.1961 7756.1 
 
 1-4 
 
 29(5.095 
 
 6976.7 
 
 7-8 
 
 304.342 7370.8 
 
 1-2 
 
 312.588 7775 6 
 
 3-8 
 
 296.488 
 
 691)5.3 
 
 97. 
 
 304.734 7389.8 
 
 5-8 
 
 312.981J 7795.2 
 
 1-2 
 
 296.881 
 
 7013.8 
 
 1-8 
 
 305.127 7408.9 
 
 3-4 
 
 313.374 7814.8 
 
 5-8 
 
 297.273 
 
 7082.4 
 
 1-4 
 
 305.520 7428.0 
 
 7-8 
 
 313.767| 7834.4 
 
 3-4 
 
 297.666 
 
 7051.0 
 
 3-8 
 
 305.913 7447.1 
 
 100. 
 
 314.159 7854.0 
 
 7-8 
 
 298.059 
 
 7069.6 
 
 1-2 
 
 306.305 
 
 7466.2 
 
 
 
 
184 
 
 WEIGHT OF ROLLED IEON. 
 
 WEIGHT OF A LINEAL FOOT OF ROUND AND SQUAKlS 
 IRON. 
 
 SIZE IN 
 INCHES. 
 
 BOUNDS. 
 
 SQUARES. 
 
 SIZE IN 
 j INCHES. 
 
 ROUNDS. 
 
 SQUARES. 
 
 WEIGHT 
 PER FOOT. 
 
 WEIGHT 
 PER FOOT. 
 
 WEIGHT 
 PER FOOT. 
 
 WEIGHT 
 PER FOOT. 
 
 & 
 
 0.01 
 
 0.013 
 
 3f 
 
 29.82 
 
 37.969 
 
 JL 
 
 0.041 
 
 0.052 
 
 3a 
 
 32.07 
 
 40.833 
 
 A 
 
 0.092 
 
 0.117 
 
 *| 
 
 34.40 
 
 43.802 
 
 i 
 
 0.163 
 
 0.208 
 
 3* 
 
 36.813 
 
 46.875 
 
 i 
 
 0.363 
 
 0.468 
 
 31 
 
 39.31 
 
 50.052 
 
 
 0.654 
 
 0.833 
 
 4* 
 
 41.887 
 
 53.333 
 
 & 
 
 1.023 
 
 1.302 
 
 4* 
 
 44.547 
 
 56 719 
 
 f 
 
 1.472 
 
 1.875 
 
 4} 
 
 47.287 
 
 GO. 208 
 
 
 2.004 
 
 2.552 
 
 41 
 
 50.11 
 
 63.802 
 
 i 
 
 2.618 
 
 3.333 
 
 41 
 
 53.013 
 
 67.50 
 
 H 
 
 3.313 
 
 4.218 
 
 4 f 
 
 56.00 
 
 71.302 
 
 U 
 
 4.09 
 
 5.208 
 
 
 59.057 
 
 75.208 
 
 U 
 
 4.947 
 
 6.302 
 
 4 
 
 62.217 
 
 79.219 
 
 H 
 
 5.89 
 
 7.50 
 
 5 
 
 65.45 
 
 83.333 
 
 if 
 
 6.01 
 
 8.802 
 
 51 
 
 68.763 
 
 87.552 
 
 11 
 
 8.017 
 
 10.208 
 
 8 
 
 72.157 
 
 91.875 
 
 11 
 
 9.203 
 
 11.718 
 
 5f 
 
 75.633 
 
 96.302 
 
 2 
 
 10.47 
 
 13.333 
 
 5 1 
 
 79.197 
 
 100.833 
 
 3| 
 
 11.82 
 
 15.052 
 
 ' 5 f 
 
 82.833 
 
 105.468 
 
 2V 
 
 13.253 
 
 16.875 
 
 
 86.557 
 
 110.208 
 
 21 
 
 14.766 
 
 18.803 
 
 5| 
 
 90.36 
 
 115.052 
 
 3* 
 
 16.36 
 
 20.833 
 
 6 
 
 94.247 
 
 120.00 
 
 81 
 
 18.036 
 
 22.969 
 
 (ji 
 
 102.263 
 
 130.208 
 
 
 19.797 
 
 25.208 
 
 6^ 
 
 110.61 
 
 140.833 
 
 3 
 
 23.56 
 
 30.00 
 
 6| 
 
 119.28 
 
 151.875 
 
 3i 
 
 25.563 
 
 32.552 
 
 7 
 
 128.28 
 
 163.333 
 
 51 
 
 27.65 
 
 35.208 
 
 
 
 
WEIGHT OF KOLLED IRON. 
 
 185 
 
 WEIGHT OF A LINEAL FOOT OF FLAT IRON. 
 
 | Width in Inches. 1 
 
 THICKNESS IN INCHES. 
 
 A 
 
 8 
 
 * 
 
 i 
 
 ft 
 
 1 
 
 * 
 
 * 
 
 SL 
 
 1 
 
 I 
 
 8 
 
 1 
 
 i 
 
 0.16 
 
 0.31 
 
 0.47 
 
 0.63 
 
 0.77 
 
 0.94 
 
 1.09 
 
 1.25 
 
 1.56 
 
 1.8* 
 
 2.18 
 
 2.50 
 
 JO. 18 
 
 0.360.55 
 
 0.73 
 
 0.91 
 
 1.09 
 
 1.28 
 
 1.46 
 
 1.83 
 
 2.19 
 
 2.5b 
 
 2.92 
 
 1 0.210.420.62 
 H 0.23(0.47,0.70 
 
 0.83 
 0.94 
 
 1.04 
 1.17 
 
 1.25 
 1.41 
 
 1.46 
 1.64 
 
 1.67 
 1.68 
 
 2. 08 
 2.34 
 
 2.50 
 2.81 
 
 2.92 
 
 3.28 
 
 3.33 
 3.75 
 
 HO. 26 
 
 0.520.78 
 
 1.04 
 
 1.30 
 
 1.56 
 
 1.82 
 
 2.08 
 
 2.60 
 
 3.12 
 
 3.64 
 
 4.17 
 
 10.29 
 
 0.57 0.86 
 
 1.15 
 
 1.43 
 
 1.72 
 
 2.00 
 
 2.29 
 
 2.86 
 
 3.44 
 
 4.01 
 
 4.58 
 
 HO. 31 
 
 0.630.94 
 
 1.25 
 
 1.56 
 
 1.88 
 
 2.19 
 
 2.50 
 
 3.13 
 
 3.75 
 
 4.38 
 
 5.00 
 
 110.34 
 
 0.681.02 
 
 1.35 
 
 1.69 
 
 2.03 
 
 2.37 
 
 2.71 
 
 3.38 
 
 4.06 
 
 4.74 
 
 5.42 
 
 HO. 36 
 
 0.73 
 
 1.09 
 
 1.46 
 
 1.82 
 
 2.19 
 
 2.55 
 
 2.92 
 
 3.65 
 
 4.37 
 
 5.10 
 
 5.83 
 
 If 0.39 
 
 0.78 
 
 1.17 
 
 1.56 
 
 1.95 
 
 2.34 
 
 2.73 
 
 3.12 
 
 3.91 
 
 4.68 
 
 5.46 
 
 6.25 
 
 2 
 
 0.42 
 
 0.83 
 
 1.24 
 
 1.67 
 
 2.08 
 
 2.50 
 
 2.92 
 
 3.33 
 
 4.17 
 
 5.00 
 
 5. as 
 
 6.67 
 
 2^0.44 
 
 0.89 
 
 1.33 
 
 1.77 
 
 2.21 
 
 2.66 3.10 
 
 3.54 
 
 4.43 
 
 5.31 
 
 6.20 
 
 7.C8 
 
 2i0.47 
 
 0.94 
 
 1.41 
 
 1.88 
 
 2.34 
 
 2.81 
 
 3.28 
 
 3.75 
 
 4.69 
 
 5.63 
 
 6.56 
 
 7.50 
 
 2f 0.49 
 
 0.991.48 
 
 1.98 
 
 2.47 
 
 2.96 
 
 3.46 
 
 3.96 
 
 4.95 
 
 5.94 
 
 6.93 
 
 7.92 
 
 2J0.52 
 
 1.041.56 
 
 2.08 
 
 2.60 
 
 3.12 
 
 3.64 
 
 4.17 
 
 5.21 
 
 6.25 
 
 7.29 
 
 8.33 
 
 2|0.55 
 
 1.091.64 
 
 2.19 
 
 2.73 
 
 3.2S 
 
 3.83 
 
 4.38 
 
 5.47 
 
 6.56 
 
 7.66 
 
 8.75 
 
 2f 0.57 
 
 1.141.72 
 
 2.29 
 
 2.86 
 
 3.44 
 
 4.01 
 
 4.59 
 
 5.73 
 
 6.87 
 
 8.02 
 
 9.17 
 
 2J0.60 
 
 1.201.80 
 
 2.40 
 
 2.99 
 
 3.59 
 
 4.19 
 
 4.79 
 
 5.99 
 
 7.19 
 
 8.38 
 
 9.58 
 
 3 
 
 0.62 
 
 1.251.87 
 
 2.50 
 
 3.12 
 
 3.75 
 
 4.37 
 
 5.00 
 
 6.25 
 
 7.50 
 
 8.75 
 
 10.00 
 
 3f0.68 
 
 1.352.03 
 
 2.71 
 
 3.38 
 
 4.07 
 
 4.74 
 
 5.42 
 
 6.77 
 
 8.12 
 
 9.48 
 
 10.83 
 
 3i0.73 
 
 1.462.19 
 
 2.92 
 
 3.65 
 
 4.38 
 
 5.11 
 
 5.83 
 
 7.29 
 
 8.75 
 
 10.21 
 
 11.67 
 
 3f 0.78 
 
 1.562.34 
 
 3.12 
 
 3.90 
 
 4.69 
 
 5.47 
 
 6.25 
 
 7.81 
 
 9.37 
 
 10.94 
 
 12.50 
 
 4 
 
 0.83 
 
 1.672.50 
 
 3.33 
 
 4.17 
 
 5.00 
 
 5.83 
 
 6.67 
 
 8.33 
 
 10.00 
 
 11.67 
 
 13.33 
 
 4*0.94 
 
 1.872.81 
 
 3.75 
 
 4.69 
 
 5.63 
 
 6.56 
 
 7.50 
 
 9.38 
 
 11.25 
 
 13.13 
 
 15.00 
 
 5 
 
 1.04 
 
 2.083.13 
 
 4.17 
 
 5.21 
 
 6.251 7.30 
 
 8.34 
 
 10.42 
 
 12.50 
 
 14.59 
 
 10.67 
 
 6 
 
 1.25 
 
 2.503.75 
 
 5.00 
 
 6.25 
 
 7.50 
 
 8.75 
 
 10.00 
 
 12.50 
 
 15.00 
 
 17.50 
 
 20.00 
 
 7 
 
 1.46 
 
 2.924.37 
 
 5.83 
 
 7.29 
 
 8.75 
 
 10.20 
 
 11.67 
 
 14.58 
 
 17.50 
 
 20.42 
 
 23.33 
 
 8 
 
 1.67 
 
 3.335.00 
 
 6.67 
 
 8.34 
 
 10.00 
 
 11.67 
 
 13.33 
 
 16.67 
 
 20.00 
 
 23.33 
 
 26.67 
 
 9 
 
 1.87 
 
 3.755.62 
 
 7.50 
 
 9.37 
 
 11.25 
 
 13.12 
 
 15.00 
 
 18.75 
 
 22.50 
 
 26.25 
 
 30.00 
 
 102.08 
 
 4.176.25 
 
 8.33 
 
 10.42 
 
 12.50 
 
 14.58 
 
 16.67 
 
 20.83 
 
 25.00 
 
 29.17 
 
 33.33 
 
 11 
 
 2.29 
 
 4.586.87 
 
 9.17 
 
 11.46 
 
 13.75 
 
 16.04 
 
 18.33 
 
 22.92 
 
 27.50 
 
 32.08 
 
 36.67 
 
 12J2.50 
 
 5.007.50 
 
 10.00 
 
 12.50 
 
 15.00 
 
 17.50 
 
 20.00 
 
 25.00 
 
 30.00 
 
 35.00 
 
 40.00 
 
186 DECIMAL EQUIVALENTS FOB FRACTIONS. 
 
 DECIMAL EQUIVALENTS FOR FRACTIONS OF 
 AN INCH. 
 
 FRACTION. 
 
 DECIMAL. 
 
 FRACTION. 
 
 DECIMAL. 
 
 * 
 
 .015625 
 
 33. 
 
 .515625 
 
 
 .03125 
 
 |l 
 
 .53125 
 
 ft 
 
 .046875 
 
 H 
 
 .546875 
 
 5s 
 
 .0625 
 
 ft 
 
 .5625 
 
 A 
 
 .078125 
 
 11 
 
 .578125 
 
 
 .09375 
 
 l 
 
 .59375 
 
 ft 
 
 .109375 
 
 II 
 
 .609375 
 
 j_ 
 
 9 
 
 .125 
 
 1 
 
 .625 
 
 J 
 
 .140625 
 
 AL 
 
 .640625 
 
 i 
 
 .15625 
 .171875 
 
 II 
 
 '. 671875 
 
 
 .1875 
 
 !i 
 
 .6875 
 
 
 .203125 
 
 fl 
 
 .703125 
 
 
 .21875 
 
 ^.a. 
 
 .71875 
 
 
 .234375 
 
 il 
 
 .734375 
 
 * 
 
 .25 
 
 4 
 
 .75 
 
 tt 
 
 .265625 
 
 h4 
 
 .765625 
 
 V 
 
 .28125 
 
 
 
 .78125 
 
 32" 
 
 .296875 
 
 ^1 
 
 .796875 
 
 5 
 
 .3125 
 
 ft 
 
 .8125 
 
 ti 
 
 .328125 
 
 f! 
 
 .828125 
 
 XI 
 
 .34375 
 
 21 
 
 .84375 
 
 II 
 
 .359375 
 
 64* 
 
 .859375 
 
 f 
 
 .375 
 
 M 
 
 1 
 
 .875 
 
 2/L 
 
 .390625 
 
 H 
 
 .890625 
 
 1 | 
 
 .40625 
 
 ft 
 
 .90625 
 
 li 
 
 .421875 
 
 
 .921875 
 
 ?y 
 
 .4375 
 
 11 
 
 .9375 
 
 ^a 
 
 .453125 
 
 H 
 
 .953125 
 
 Vs 
 
 .46875 
 
 31. 
 
 .96875 
 
 fi 
 
 .484375 
 
 It 
 
 .984375 
 
 
 .5 
 
 
 
STANDARD SEPARATORS FOR PENCOYD BEAMS. 187 
 
 STANDARD SEPARATORS FOR PENCOYD I BEAMS. 
 
 CHART 
 No. 
 
 SIZE OF BEAM. 
 
 Weieht of 
 separator. 
 
 JS 
 
 -S 
 
 5 K^ 
 
 s* 
 ill 
 jr-s 
 
 BOLTS, A. 
 
 Weight of each 
 complete bolt. 
 
 jjf 
 
 No. 
 
 SIZE. 
 
 1 
 
 15 " Heavy 
 
 22 
 
 3.84 
 
 2 
 
 r 
 
 1.75 
 
 .123 
 
 2 
 
 15 " Light 
 
 21 
 
 3.13 
 
 2 
 
 3." 
 
 1.62 
 
 .123 
 
 3 
 
 12 " Heavy 
 
 16 
 
 2.76 
 
 2 
 
 " 
 
 1.69 
 
 .123 
 
 4 
 
 12 " Light 
 
 14? 
 
 2.95 
 
 2 
 
 li" 
 4 
 
 1.58 
 
 .123 
 
 5 
 
 10" Heavy 
 
 in 
 
 2.10 
 
 1 
 
 3." 
 4 
 
 1.64 
 
 .123 
 
 51 
 
 lO.f" Medium 
 
 11 
 
 2.06 
 
 1 
 
 2" 
 4 
 
 1.28 
 
 .123 
 
 6 
 
 10|" Light 
 
 11 
 
 2.03 
 
 1 
 
 1" 
 
 1.53 
 
 .123 
 
 7 
 
 10 " Heavy 
 
 10 
 
 1.93 
 
 1 
 
 " 
 
 4 
 
 1.56 
 
 .123 
 
 8 
 
 10 " Light 
 
 10 
 
 1.93 
 
 1 
 
 r 
 
 1.52 
 
 .123 
 
 9 
 
 <J " Heavy 
 
 QL 
 
 1.63 
 
 1 
 
 t" 
 
 1.52 
 
 .123 
 
 10 
 
 9 " Light 
 
 9 
 
 1.63 
 
 1 
 
 r 
 
 1.48 
 
 .123 
 
 11 
 
 8 " Heavy 
 
 6| 
 
 1.36 
 
 1 
 
 
 1.50 
 
 .123 
 
 12 
 
 8 " Light 
 
 6i 
 
 1.49 
 
 1 
 
 4 
 
 1.46 
 
 .123 
 
 13 
 
 7 " Heavy 
 
 4 
 
 1.26 
 
 1 
 
 fi." 
 
 0.96 
 
 .085 
 
 14 
 
 7 " Light 
 
 4 
 
 1.26 
 
 1 
 
 1" 
 
 0.91 
 
 .085 
 
 15 
 
 6 " Heavy 
 
 3 
 
 1.24 
 
 1 
 
 8"" 
 
 0.90 
 
 .085 
 
 16 
 
 6 " Light 
 
 3 
 
 1.24 
 
 1 
 
 t;| 
 
 0.87 
 
 .085 
 
 17 
 
 5 " Heavy 
 
 2f 
 
 1.10 
 
 1 
 
 
 0.43 
 
 .055 
 
 18 
 
 5 " Light 
 
 2J 
 
 1.10 
 
 1 
 
 i" 
 
 0.42 
 
 .055 
 
 19 
 
 4 " Heavy 
 
 2 
 
 0.85 
 
 1 
 
 i" 
 
 0.42 
 
 .055 
 
 20 
 
 4 " Light 
 
 2 
 
 0.85 
 
 1 
 
 i" 
 
 0.39 
 
 .055 
 
 21 
 
 3 " Heavy 
 
 1^. 
 
 0.69 
 
 1 
 
 i" 
 
 0.38 
 
 .055 
 
 22 
 
 3 " Light 
 
 il 
 
 0.69 
 
 1 
 
 r 
 
 0.31 
 
 .055 
 
 The figures in the third column are the weights in Ibs. for cast iron sepa- 
 rators suitable for beams, placed with flanges in contact. When the flanges 
 are separated, add the amount corresponding to the distance of separation, 
 given in the fourth column. In the same way the weight of bolts may be 
 obtained in the final columns. 
 
 Example. A pair of 12" heavy beams have the flanges separated H inches, 
 the weight of one separator will be 2.76 x H + 1(5 = 20.14 Ibs. One f bolt 
 complete and suitable for close flanges, will weigh 1.G9 Ibs. Add to this .123 
 x 1 = 1.88, which is the weight of bolt required. 
 
188 
 
 BOLTS AND NUTS. 
 
 BOLTS AND NUTS. 
 MANUFACTURER'S STANDARD. 
 
 
 
 
 
 WEIGHT 
 
 OP HEAD 
 
 WEIGHT 
 
 Si 
 
 ZE OP Nu 
 
 T 
 
 
 
 
 
 
 
 
 DlAMETEK 
 
 AND 
 
 NUT. 
 
 OP BOLT 
 
 
 
 
 Of 
 
 
 
 BODIES 
 
 
 
 
 
 
 
 PER INCH 
 
 Width. 
 
 Thick- 
 ness. 
 
 Hole. 
 
 BOLT. 
 
 Square. 
 
 Hexagon. 
 
 OF 
 
 LENGTH. 
 
 I 
 
 A 
 
 1 
 
 A 
 
 .034 
 .067 
 
 .031 
 .055 
 
 .014 
 .021 
 
 
 
 1 
 
 A 
 
 .110 
 .181 
 
 .105 
 .171 
 
 .031 
 .042 
 
 1 
 
 t 
 
 
 f 
 
 .210 
 
 .192 
 
 .055 
 
 1 
 
 ^ 
 
 r. 
 
 1 
 
 .280 
 
 .233 
 
 .055 
 
 H 
 
 j^. 
 
 i 
 
 
 .369 
 
 .335 
 
 .069 
 
 4 
 
 1 
 
 * 
 
 b. 
 
 .431 
 
 .403 
 
 .085 
 
 u 
 
 5. 
 
 
 5. 
 
 .545 
 
 .475 
 
 .085 
 
 if 
 
 a. 
 
 
 
 
 563 
 
 .085 
 
 *f 
 
 I 
 
 
 
 .776 
 
 .673 
 
 .123 
 
 l 
 
 i 
 
 
 
 
 .770 
 
 .123 
 
 ll 
 
 i 
 
 
 
 
 .964 
 
 .123 
 
 if 
 
 1 
 
 
 
 1.34 
 
 1.14 
 
 .167 
 
 l| 
 
 1 
 
 3-5- 
 
 i 
 
 
 1.19 
 
 .167 
 
 
 1 
 
 fft 
 
 i 
 
 
 1.28 
 
 .167 
 
 j| 
 
 
 37 
 
 1 
 
 1.46 
 
 
 .167 
 
 l| 
 
 i 
 
 ? 
 
 
 1.75 
 
 1.48 
 
 .218 
 
 13- 
 
 u 
 
 
 1 
 
 
 1.65 
 
 .218 
 
 2* 
 
 l 8 
 
 1 
 
 1 
 
 2.24 
 
 
 .218 
 
 2 
 2 
 
 l| 
 
 ft 
 
 | 
 
 2.47 
 
 2:48* 
 
 .276 
 .276 
 
 o i 
 
 1 
 
 44 
 
 1 1 
 
 3 14 
 
 
 276 
 
 2i 
 
 ll 
 
 ID 
 
 jl 
 
 3.'74 
 
 
 .341 
 
 4 
 
 if 
 
 1-jlg. 
 
 l| 
 
 
 3'.46 
 
 .341 
 
 01 
 
 1"4 
 
 ITF 
 
 H 
 
 4.47 
 
 
 
 .341 
 
 2| 
 
 H 
 
 IfV 
 
 li 
 
 
 4.63 
 
 .412 
 
 2J 
 
 If 
 
 1'fV 
 
 l| 
 
 5.85 
 
 
 
 .412 
 
 2| 
 
 H 
 
 1'rff 
 
 H 
 
 
 6.11 
 
 .491 
 
 3 
 
 
 IA 
 
 
 7.59 
 
 
 
 .491 
 
BOLTS AND NUTS. 
 
 189 
 
 BOLTS AND NUTS. 
 MANUFACTURER'S STANDARD. 
 
 
 
 WEIGHT OF HEAD 
 
 WEIGHT 
 
 SIZE OF NUT. 
 
 
 
 
 
 DIAMETER 
 
 AND NUT. 
 
 OF BOLT 
 
 
 
 
 BODIES 
 
 
 
 
 OP 
 
 
 
 PER INCH 
 
 Width. 
 
 Thick- 
 
 liCSS. 
 
 Hole. 
 
 BOLT. 
 
 Square. 
 
 Hexagon. 
 
 OF 
 
 LENGTH. 
 
 3 
 
 1} 
 
 liV 
 
 If 
 
 
 7.65 
 
 .570 
 
 
 If 
 
 1'Hf 
 
 If 
 
 (K48 
 
 .... 
 
 .576 
 
 &* 
 
 H 
 
 1 -i^ 
 
 lj 
 
 
 9.42 
 
 .668 
 
 3? 
 
 If 
 
 1-1% 
 
 If 
 
 li.'9 
 
 
 .668 
 
 3? 
 
 2 
 
 1H 
 
 H 
 
 .... 
 
 li.'e' 
 
 .767 
 
 P 
 
 If 
 
 2 
 
 1 
 
 If 
 
 2 
 
 14.1 
 
 12^6 
 
 .767 
 .872 
 
 3* 
 
 2 
 
 Mi 
 
 2 
 
 .... 
 
 12.6 
 
 .872 
 
 4 
 
 2 
 
 Ht 
 
 2 
 
 18.6 
 
 .... 
 
 .872 
 
 4 
 
 2* L 
 
 H 
 
 2$ 
 
 18.9 
 
 .... 
 
 .985 
 
 4 
 
 *i 
 
 2 
 
 5J 
 
 19.3 
 
 .... 
 
 1.104 
 
 
 The preceding tables for bolts and nuts include the sizes of 
 nuts usually applied to structural work. 
 
 The sizes known as " U. S." or " Franklin Inst." standard, 
 used on finished machines, are lighter than the foregoing. 
 
 The weights given in the fifth and sixth columns are for a 
 head and nut, or for two nuts, including the portion of the bolt 
 body contained in the nuts. 
 
 The final column is the weight of bolt bodies of round iron per 
 inch of length. To obtain the weight of any bolt : multiply the 
 amount in final column by the clear length between nuts in 
 inches and add in the weight of nuts as given in the fifth or sixth 
 column. 
 
 Example. What is the weight of a bolt f" diam. .and 20" 
 long between nuts, the nuts being If" sq. x |" ? .123 x 20 = 
 2.46 + .77 = 3.23lbs. 
 
190 WEIGHT OF BRIDGE RIVETS IN POUNDS. 
 
 WEIGHT OF BRIDGE RIVETS IN POUNDS 
 
 DIAMETER or KIVET. 
 
 WEIGHT OP Two HEADS. 
 
 WEIGHT OF BODY PER 
 INCH OF LENGTH. 
 
 t 
 
 .036 
 
 .031 
 
 A 
 
 .058 
 
 .OJ2 
 
 J 
 
 .080 
 
 .054 
 
 & 
 
 .120 
 
 .069 
 
 1 
 
 .160 
 
 .085 
 
 & 
 
 .210 
 
 .103 
 
 t 
 
 .260 
 
 .123 
 
 it 
 
 .350 
 
 .144 
 
 1 
 
 .440 
 
 .167 
 
 H 
 
 .540 
 
 .192 
 
 i 
 
 .640 
 
 .218 
 
 ttir 
 
 .714 
 
 .246 
 
 11 
 
 .788 
 
 276 
 
 i* 
 
 1.07 
 
 .341 
 
 This table applies to rivets whose heads are a spherical seg- 
 ment, the contents being equal to a hemisphere whose diameter 
 equals 1| diameters of the rivet shank plus -f^th of an inch. 
 To find the weight of rivets, take the total thickness of material 
 to be riveted, which will be the length of the rivet between 
 heads, and multiply this by the weight per inch of length of 
 rivet shank, and add in the weight of the two heads. 
 
 Example. Three f inch plates are to be riveted together with 
 | inch rivets, required the weight of each rivet. The length of 
 rivet shank equals 3 x f = 2k inches. Then 2i x .167= .376, 
 to which add the weight of the heads .44, making .816 Ib. for 
 each rivet. 
 
INDEX. 
 
 Angle bars, explanation of tables of dimensions 1 
 
 " " weights per yard of various thicknesses 8, 9 
 
 Angles, sq. root, weights per yard of various thicknesses 10 
 
 Angle covers " " " " " 13 
 
 " bars, elements of even legged 98 
 
 " " " uneven legged 99 
 
 " " moment of inertia 98, 99, 104 
 
 " radius of gyration 98, 99, 104, 113 
 
 " "as struts and tables of safe loads 135-140 
 
 " " acute for cable roads 16 
 
 " " approximate rule for beams 69 
 
 Areas and circumferences of circles 178-183 
 
 Axles, "Master Car Builder's Standard " 15 
 
 Beams, explanation of tables of dimensions 1 
 
 " I, dimensions of minimum and maximum sizes 2 
 
 " I, weights of various web thicknesses 3 
 
 " elements of I section 92, 93 
 
 " moments of inertia 92-96, 105, 106 
 
 " radii of gyration 92-96, 105, 106, 113 
 
 " maximum load in tons 90 
 
 " factors of safety 34 
 
 " greatest safe loads 35 
 
 " deflection of 37 
 
 " limits for safe load 33 
 
 " " " deflection 39 
 
 " table of safe loads and deflections for 1 40-45 
 
 " unsymmetrical sections 34 
 
 " without lateral support 36, 73 
 
 " with fixed ends 38, 39 
 
 " continuous 38, 39, 75-77 
 
 " cantilever 38, 74-77 
 
 " iron floor. . . .52-55 
 
192 INDEX. 
 
 Beams, tables of safe loads and spacing for floors 58-62 
 
 " approximate rules for strength of various sections. 68, 69 
 
 " bending moments 78-81 
 
 " subject to both bending and compression 84 
 
 " support, brick walls 65, 66 
 
 " " irregular loads 82,83 
 
 Beam sections as struts. Tables of safe loads 124-134 
 
 Belting 175 
 
 Bending moments for beams 78-81 
 
 " resistance of iron to 32 
 
 Brick arches for floors 54 
 
 " tie rods for 63 
 
 " walls, beams for supporting 65, 66 
 
 Bulb plates 16 
 
 " iron . . . (See Deck Beams.) 
 
 Cantilever beams 38, 74-77 
 
 Channel bars, explanation of tables of dimensions 1 
 
 " " dimensions of minimum and maximum sec- 
 tions 4 
 
 " " weight of various web thicknesses -, 
 
 " " Car Builder's section 16 
 
 " " elements of 94, 95 
 
 " " moments of inertia 94, 95, 105 
 
 " " radii of gyration 94, 95, 105 
 
 " " tables of safe loads and deflections 46-49 
 
 " " struts 121-122 
 
 " " as struts. Tables of safe loads 144-153 
 
 " " approximate rule for beams 69 
 
 Circles, areas and circumferences 178-183 
 
 Columns of wrought iron .154-159 
 
 " safe loads for round 156, 157 
 
 " "square 158,159 
 
 Compression, wrought iron in 18-22 
 
 Continuous beams 38, 39, 75-77 
 
 Cover angles, weight per yard of various thicknesses 13 
 
 Crane stresses 163, 164 
 
 Decimal equivalents for fractions of an inch 186 
 
INDEX. 193 
 
 Deck beams, dimensions of minimum and maximum sections 6 
 " weights per yard of various web thicknesses. . . 7 
 
 " " elements of 97-97 
 
 " " moments of inertia 96, 97, 106 
 
 " " radii of gyration 96,97,106 
 
 " " formula for resistance to bending 35 
 
 ' " tables of safe loads and deflections 50, 51 
 
 " " " " " " and spacing for floor 
 
 beams 56, 57 
 
 " u approximate rule for beams 69 
 
 Deflection of iron beams 37 
 
 "steel " 27 
 
 " limits of, for beams 39 
 
 " tables of, for I beams 40-45 
 
 " " " " channel bars.. 46-49 
 
 " " " " deck beams 50,51 
 
 for beams .' 78-81 
 
 of shafting 173 
 
 Elasticity of wrought iron 19-22 
 
 Elements of structural shapes 87-91 
 
 " " " " tables ..92-101 
 
 Factors of safety for beams 34 
 
 " " " " struts 116-117 
 
 " " ' " shafting 171 
 
 Flat bar iron, widths and thicknesses 14 
 
 " " " approximate rule for beams of 63 
 
 Flexure (See Deflection.) 
 
 Floor Beams 52-55 
 
 " " rule for weights of 53 
 
 " " spacing of 54 
 
 " ' ' lateral strength 63 
 
 Formulae for unsymmetrical beams 35 
 
 ' ' approximate, for rolled beams 67 
 
 " tables of, for beams of various sections 68, 69 
 
 Fractions of an inch expressed in decimals 186 
 
 Girder stresses 165-166 
 
 Gyration, radius of 87-88 
 
194 
 
 INDEX. 
 
 Gyration, radius of, for various sections 92-101 
 
 " " formulae for various sections 102-111 
 
 " tables 112,113 
 
 " for round columns 155 
 
 " " " square " 155 
 
 Half-round bar iron, sizes 14 
 
 Horse-power of shafting 173 
 
 I beams (See Beams ) 
 
 Inertia, moments of 87-88 
 
 " " " tables for various sections 92-101 
 
 " " " formulae for various sections 102-111 
 
 " " " for combined sections 108-111 
 
 Iron, ' < Pencoyd High Test " 15 
 
 " "Pencoyd Refined" 15 
 
 " strength of wrought 17 
 
 " ductility of 17 
 
 " resistance to compression 18 
 
 " elasticity of rolled 19 
 
 " tensile and compressive tests 20-22 
 
 " resistance to shearing 23 
 
 "torsion 23 
 
 " " " bending 32 
 
 " columns 154-159 
 
 " shafting , 170-175 
 
 " struts 114-159 
 
 " sizes of bars ' 14 
 
 " weight per lineal foot of bars 184-185 
 
 Lateral strength of floor beams 63 
 
 " support, beams without 36, 73 
 
 Latticing for channel struts 121, 144-149 
 
 Loads (See Safe Loads.) 
 
 Modulus of elasticity of rolled iron .19-22, 89 
 
 < "steel 26,27 
 
 " " resistance for steel 26, 27 
 
 " ' ' rupture for rolled iron 32 
 
 Pins and rivets. . ... .160-162 
 
INDEX. 195 
 
 Bails, miner's track 16 
 
 " splice bar for do. do 16 
 
 ' * for slot of cable roads 16 
 
 Rivets and pins 160-1(52 
 
 Roof stresses 167-169 
 
 Round bar iron, sizes 14 
 
 " " " approximate rule for beams of 68 
 
 Rule for weight of rolled iron 15, 68 
 
 " " " " iron in floor beams 53 
 
 " " thrust of brick arches 63 
 
 " " lateral strength of I beams 63, 64 
 
 " " < " " channel bars 63,64 
 
 " " beams bearing irregular loads 82 
 
 Rules, approximate for moments of inertia 107 
 
 " for shafting ..170-175 
 
 Safe load, co-efficient for 88 
 
 " loads, limits of. for beams 33 
 
 " " greatest, for beams 35 
 
 " " " I beams 40-45 
 
 "deckbeams 50-51 
 
 " " " channel bars 46-49 
 
 " " for iron struts of any section 119 
 
 " " " " " tables of, for beams, channels, 
 
 angles and tee sections 123-159 
 
 " " for columns 156-159 
 
 Shafting, wrought iron 170-175 
 
 " tables of diameters and lengths 176, 177 
 
 Shearing strength of wrought iron 23 
 
 Slot rail for cable roads 16 
 
 Spacing of floor beams 54 
 
 " " " " tables of, for eyebeam sections. . . .58-62 
 " " " " " " " deck beam sections.. 56-57 
 
 Specific gravity iron and steel 30 
 
 Splice bars for miner's track rail 16 
 
 Square bar iron, sizes 14 
 
 " root angles, weights per yard of various thicknesses. 10 
 
 Steel, tensile strength 24-26 
 
 " compressive strength 24-26 
 
 ' transverse " ..27-28 
 
196 INDEX. 
 
 Steel, deflections of beams 27 
 
 " modulus of elasticity 27 
 
 " beams 93 
 
 " shafting 29 
 
 " struts 29, HO, 123 
 
 Stresses in framed structures 163-169 
 
 Structural steel 24 
 
 Struts of rolled iron. 114 159 
 
 " steel 29,50,123 
 
 " factors of safety for 116, 117 
 
 " table of ultimate resistance for iron 118 
 
 " greatest safe loads for iron of any section 119 
 
 " tables of safe loads for beam sections 124-134 
 
 " " " " " angle " 138-140 
 
 " '" " " * tee " 142-143 
 
 " " " " " channel sections 144-153 
 
 Tee bars, explanation of tables of dimensions 1 
 
 " " weights and dimensions of even- legged 11 
 
 " " " " " " uneven-legged 13 
 
 " " elements of even-legged 100 
 
 " " *' *' uneven-legged 101 
 
 " "- moments of inertia 100,101,104 
 
 *' " radii of gyration 100, 101, 104 
 
 " " as struts and tables of safe loads 141-143 
 
 " " approximate rule for beams. 69 
 
 Tension in wrought iron 17-22 
 
 Tie rods for brick arches 63 
 
 Torsional strength of wrought iron 23 
 
 Ultimate loads for iron struts 118 
 
 " " "steel ' 31 
 
 " resistance of iron to bending stress 32 
 
 Weight per lineal foot of round and square iron 184 
 
 " " " " "flat iron 185 
 
 Weight of cast iron separators 187 
 
 bolts and nuts 188-189 
 
 " rivets . . .190 
 
PENEDYD SHAPES 
 
 Plate 1 
 Plates 2 tn2B Scaled Size 
 
Plate Nn. I 
 
 Nn.l 
 Wt. 2DD to 233 Lbs, 
 
 Nn. 2 
 Wt. 143 to 2DI Lhs. 
 
 ~^^ 
 
 
 All weights ^iven in pounds perYard. 
 
Plate Nn. 2 
 
 Wt. IBB tn 134 Lhs. 
 
 weights ivEn in pounds peirYard. 
 
PlatE Nn. 
 
 Alt weights iven in pounds perYard. 
 Wi. 134:. tn IBl.lbs. 
 
 ti* 
 
 Wt. 1QB. tn 13S.Lhs. 
 
 -5V,- 
 NQ. S 
 
Plate Na-4- 
 
 Wt.BH.tn l.U9.Lhs. 
 
 Na.Sl 
 
 Na. B 
 
 No. 22 
 Wt.17 taZZLbs, 
 
 *~ * >3$: 
 
 All weights iven in pounds perYard. 
 

Plate Nn. .5 
 
 Wt. 112 tn 137. Lbs. 
 
 S 
 
 Nn.7 
 
 Wt. BD to !D6Lbs. 
 
 H? 
 
 
 Nn. B 
 All weights iven in pounds perYard. 
 
 -;v W - 
 
 ..*! 
 
Plate Nc. B 
 
 Wt.34 tn 4DLhs. Wt.3D tn 4D Lhs. 
 
 pp 
 
 Nn.!7 
 
 Na. IB 
 
 Wt.eD fn 22 Lhs. Wt. 7D tn BB Lhs. 
 
 ND. a 
 
 05 
 
 N D. I D 
 
 All weights ^iven in pounds perYard. 
 
Plate Ha. 7 
 
 Wt..5d tn B3 Lhs. Wt. 4D to E3 Lhs. 
 
 NnlS 
 
 * 
 
 Nn.lB 
 
 < 3% - <- 3*-~ -> 
 
 Wt.Bl tn IDB.3 Lbs: Wl.'BS tn 75 Lhs. 
 
 Nn.ll 
 
 & 
 
 00 
 
 N a. 1 2 
 
 All weights ^iven in pounds pet: Yard. 
 
Flats Nn. B 
 
 Nnl3 
 WtBS to BB Lbs. 
 
 Wt.Sl to BB Lbs, 
 
 Nn.13 NaZD 
 
 Wt. 28 ta 38 Lbs, Wt-IS.S tp 2I.S Lbs. 
 
 -sty 
 
 All weights ^iven in pounds pei:Yard. 
 
Plate Nn. H 
 
 ND. 3D 
 
 h 
 
 Nn.33 
 
 in 
 
 in 
 
 J3 
 
 a 
 LG 
 
 All weights ^iven in pounds perYard. 
 
Plate Nn. ID 
 
 No. 32 
 
 Nn.3I 
 
 All weights ivEn in pounds perYard. 
 
Plate No. I! 
 
 All weights ^iven in pounds perYard. 
 
 '3 2 
 
Plate No. 12 
 
 Nn. 36 
 
 Nn. 37 
 
 
 B I 
 
 Nn. 38 
 
 Wt. 43 tn BD.5 Lbs, 
 
 Nn. 3 3 
 Wt. 3D tn 54 Lhs. 
 
 ff 
 
 All weights ^iven in pounds perYard. 
 
Plate Nn.13 
 
Plate Nn. 
 
 2 
 
 All weights iven in pounds perYard. 
 
Plate Nn.lS 
 
 All weights iven in pounds perYard. 
 
Plate Na.lB 
 
 Na.E4 
 
 No.ES 
 
 m 
 
 ra 
 
 No, B7 
 
 "in 
 
 DJ 
 
 No.GB 
 3% 
 
 All weights ^iven in pounds perYard. 
 
Plate NQ. 17 
 
 Wt.3.fi.5 Lbs. 
 4" 
 
 Wt.3 Lbs. 
 
 No.7D 
 
 Wt.3 Lbs. 
 
 * 
 
 No.71 
 
 Wt. ZE.Lbs. 
 $>.... 
 
 ND.BI 
 
 Wt.ia.5 Lhs. 
 
 '-,-- -2% 
 
 1%'~~ 
 
 Nn.72 
 
 ND.BD 
 
 Na.73 
 
 Wt.17. 52 Lhs. Wt.B Lhs. Wt.11.7S Us. 
 
 - " 5 
 
 Nn.75 
 
 Wt.IZ Lhs. Wt.7.I Lhs. 
 
 NnJB 
 
 NnJB 
 
 Wt.lD.S Lbs. 
 
 o 
 
 Nn.77 
 
 All weights &\ven in pounds perYard. 
 
Plate Nn. IB 
 
 Wt. ZZ-.E Lbs. 
 
 ~ r^n 
 
 ' *I * " ! 
 
 ND.B3 
 
 Wt.19.3 Lbs. 
 
 Na.BZ 
 
 All weights ^iven in pounds perYard. 
 
Plate Nn.lS 
 
 Wt. 44. I Lhs. 
 
 Wt.2D..4Lfas. 
 
 IS/' 
 
 3**V 
 
 Np.lDY 
 
 ^ 
 
 tv _, 
 
 Wt. 48,^44 Lbs, 
 
 I ^ . fc* J 
 
 xr- % - ,- 
 
 Nn 
 
 .IDE 
 
 Wt.11.2 Lbs, 
 
 J* 
 
 ^ 1 
 
 Nn.9B 
 
 Wt.2&.2SLhs. 
 
 Na.37 
 
 Wt.23.7S Lhs. 
 
 Wt.lB.7SLhs. 
 
 Wt. 21. Lhs. 
 
 ------- 2%-- 
 
 Nn.lD4 
 
 NQ. ins 
 
 All weights ^iven in pounds perYard. 
 
Plate ND. 2D 
 
 Wt.44-S Lhs. 
 
 Wt.4LB Lhs. 
 
 
 Nn.an 
 
 Wt.7 Lhs. 
 
 Wt.3.1 Lhs. 
 
 Wt. 3D. 7 Lhs.. 
 
 Wt.B ; 7SLhs. 
 Nn.92 <_ ...... -2' ..... --> 
 
 Wt. 33. Lhs. 
 
 ----- J* 
 
 Nn.lD3 
 
 Wt.25.H Lhs. 
 
 No. 94 
 
 Wt.ZS.ZS Lhs. 
 
 Nn.95 
 
 i_._.J 
 All weights ivEn in pounds perYard. 
 
Pi ate No. 21 
 
 Wt.38.5 Lhs. 
 --4' 
 
 Wt.ZD.B Lbs. 
 
 15*4 
 
 Nn.lll 
 
 No.ina 
 
 Wt. 17.7 Lbs. 
 
 All weights ^iven in pounds perYard. 
 

 Plate Nn.ZS 
 
 Na.l2Q 
 
 No. 129 
 
 Na.132 
 
 ^L\ 
 
 AH weights ^iven in pounds perYard. 
 
Plate Nn.23 
 
 Nal54 
 
 Nn.152 
 
 No.l4D 
 
 NfclSt 
 
 Na.153 
 
 Na. 141 
 
 Na.142 
 
 Ka.143 
 
 All weights ^iven in pounds perYard. 
 
Plate ND. 2-q- 
 
 Na.lSD 
 
 ND.I5S 
 
 Nn.lSB 
 
 Nn.I57 
 
 All weights ^iven in pounds perYard. 
 
Plate ND. 
 
 NQ.IHD 
 
 Nn.171 
 Alt weights ivEn in pounds perYard. 
 
Plate Nn.ZB 
 
 Nn.lBD Nn.lBI Nn.lB2 Nn.lB3 
 
 All weights ^iven in paunds perYard. 
 
Plate No. 2 7 
 
 Nn.lBl WtS.2Lba 
 
 Nn.190 Wt.ZS Lbs, 
 
 Wt.SB L-hs ' No. 192 
 
 No. 134. 
 
 Nn.lB3. 
 
 * 
 
 Wt.4.3 Lhs.p. Y2rd. Wt 4.3 Lhs. p. Yard. 
 
 Nn 135 5 
 
 ND. me 
 
 Nn. 197 
 
 No. 19B 
 
 ' 2D,a tn 34.5 Lbs. 
 
 All weights ^iven in pounds perYard. 
 

Plate No. 28 
 
 METHOD OF INCREASING 
 SECTIONAL AREAS. 
 
 Cross-hatched portions represent 
 
 the minimum sections, and the 
 
 blank portions the added areas. 
 
 W, 
 
 All weights ivEn in pounds perYard. 
 


 
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